Thanks Dr J.  I think I now have too much information , lol.  but the calculator helped make sense of it.
 
Going to see tyre man tomorrow & tell him that he told me the wrong info, ask him nicely to take the wrong tyres back & replace them with the 205/55R15 for not much extra money.
 

Dr.J

The second number in tyre sizes is the percentage of width the sidewall has.
I'll explain...
Say you have a 205/50 R16 tyre, the '50' means 50% of 205 or the tyre's overall width called 'Section Width'.
So; 205mm width, 50% sidewall = sidewall has an overall height of 102.5mm. This includes the bit that you can't see inside the wheel holding the tyre to the wheel.
Pretty much all tyres are measured this way with the exclusion of some 4WD, truck and heavy machinery tyres.
Here's a link to figure out 'Rolling Diameters' so your speedo reads correctly with your wheel and tyre choice... http://www.kouki.co.uk/utilities/visual-tyre-size-calculator
Have fun! :)

Haven't been to the tyre guys, yet.  But I emailed the guy I bought the car from to ask if he could remember what he had on the back.  He is fairly sure he had 225/55R15.  He also said the he used to get the same thing everytime he went to get tyres.  They would try to talk him into changing them.
He had used 205's, but ended up with 225's the last couple of changes.
I'll keep you posted.

I went in to the tyre place after work & the guy on the counter checked the placard & also is a Toyota approved mechanic & new straight away that the tyres on the back were wrong.  He then checked a rather large catalogue & found that the new recomendation is 215/55/R15.  He also got one of the other guys who was at the counter to check the gordean site even though they don't use it anymore. 
When he checked to see who had sold me the tyres, it was the boss, who wasn't there today.  He said it could have been because of a stock issue or something.  But at the time the only thing "the boss" said was that they should all be the same, didn't say anything about stock.  So the guys I talked to today couldn't make any sort of decision without speaking to the boss.  So I'm expecting a call tomorrow. 
I'm hoping that they exchange for 215's with me paying the difference of what it would have been.  Considering they made the mistake.
 

Hi,
They are Toyo.  The ones they originally put on are described on the invoice as: 195/55/R15 TEO Plus 85V.  Waiting for their call & was thinking that they'd probably replace with 215/55/R15.  The price I paid for the 195's was $159 each plus a 4 wheel alignment.  So I'm hoping the extra for 215's won't be too much.  And would hope they don't charge again for the alignment, seeing as how it was their mistake.

Gatesys SW20

Hmm sounds good what type of tyres are they? Toyo what?
And how much do you know
What are they exactly 215/55(wxv)will be a number then 15 for 15 inch
Just curious is all ahah

Shaz,  I don't know where your tyre people got their info, but a 215/55R15 is the wrong size for an MR2 15 inch rear.
 
The correct OEM MR2 rear tyre size is 225/50R15 and was fitted to a 7 inch wide rim.
If a 215/55R15 tyre was fitted it would almost certainly be less stable (bring a higher profile and not wide enough) and would also put your speedo out because the diameter is too large.
 
Also you need to know that the 225/50R15 size if not that common and there are limited choices of brands available, but they are around if you look for them.
 

Have the guys that fitted your tyres check the rim width and offsets front and back. They will be stamped on the inside of the wheels and the tyres guys will definately know how to find them. As you are not running factory wheels, factory recomendations really are of no relevance to you anymore for tyre size. I reckon you have +35 offset wheels and only 6inch wide rims all around explaining why they have fitted 195's all around. If your rim size is 7inches wide at the rear however then definately have them fit 225's at the rear. 225's aren't recommended for 6inch wide wheels. the widest allowable on a 15x6 is 215 with optimal being listed as a 195 on a 6inch rim by Bridgestone.

track_mr2
...The problem with having the same offsets and width front and rear on an MR2 is that the front wheel track will be wider then the rear.

 
Just to clarify, wheel width does not affect vehicle track, it is determined by wheel offset.  Stock SW20 offset is 45mm front and back, regardless of the width of the wheels, if you retain this offset the track will remain unchanged.
 
Yes tyre width should be matched to wheel width for optimum performance, and there is usually 1 inch or so margin of allowable wheel width for a given tyre width.  The tyre manufactures have tables showing appropriate wheel widths.
 
My first SW20 had 15x7 all round with the same off set, I ran the stock size of 195/55/55 F and 225/50/15 R (later replaced fronts with 205/50/15) for many years and kms with no issues and great handling (the front 205 reduced understeer on slower corners and wasnt as stretched on the rim as the 195).
 
As stated by others, get the correct tyre size required (assuming your wheels are not to narrow in width), otherwise look for a more correct set of wheels and fit the correct tyres.  It was poor (and probably illegal) for the shop to fit incorrect tyres, sounds like they dont know what they are talking about.  The handling of the MR2 can be tricky at the limit (especially for the uninitiated), you dont want to compromise things unnecessarily.
 
The stock wheel and tyre sizes for SW20 are as follows:
 
Early cars
F: 14x6, +45 w/ 195/60R14
R: 14x7, +45 w/ 205/60R14

Later cars
F: 15x6, +45 w/ 195/55R15
R: 15x7, +45 w/ 225/50R15

 
Cheers