Lefty Help

Hello everyone, I am new to Ukulele Underground and to the Uke as well! I was hoping someone could help me out. I ordered a Lyon by Washburn LU5 and asked the seller to flip the strings because I must play lefty. I talked with him personally on the phone and he said this was no problem. However, I'm not really sure if he did! I emailed him to ask if he had done it, and has yet to reply (three days ago). My question is: is it possible to tune the uke for a lefty without switching the strings (because mine is definitely tuned lefty). Whenever I hold the ukulele in playing position for me, it seems that the thinnest string is closest to my head. Is that correct?
My only concern is that I may be doing something wrong to the strings if they are not in the right order for me. Sorry for the long post!

If it is re-entrant tuned it would seem that way. The G (top) string is the second thinnest string. It should go GCEA top to bottom as you hold it. I have my ukes strung lefty, one re-entrant and one Low-G. You might want to get a clip on tuner. It will make life easier and your uke will sound better in tune.

Here is an example of string gauges for re-entrant Worth clear medium strings.
A .0205"(.52mm), E .0260"(.66mm), C .0291"(.74mm) G .0224"(.57mm).

Pretty sure it'd be impossible to re-tune the strings to lefty, flipping them over only takes 5 minutes. From the top, the second string down should be the thickest. The third string from the top (next one down) should be the second thickest. The top and bottom strings are thin and fairly similar.

If not, it's wrong.

Thank you both so much! I had my suspicions all along that they never re-strung it, so I just got done re-stringing it myself. That was my first time ever stringing any instrument and it was surprisingly pretty easy! I will look into getting a clip-on tuner. Thanks again!