I'm not sure about this translation. In English, "it's nothing" and "you're welcome" are not the same. Yes, they are both often acceptable in response to "thank you", but there is a real difference. "It's nothing" is much more casual and can be taken as being dismissive of the person's thanks. I don't know if the same is true in Turkish, but it would be nice to know before I offend anyone by saying bir şey değil.
"bir şey değil" would not be taken dismissive at all, it is a nice answer to thank you. I only noticed one place it is not ideal to use it; when someone thank you for something that you had to do anyway. For example if I thank the waiter for bringing my food, it is weird if he says "bir şey değil". He might say "rica ederim", or even better "afiyet olsun".
This most common of courteous replies... is most commonly said after someone says "thank you" for you doing something for them.
Therefore because your action has already taken place that you were being thanked for... "It was nothing" is the correct translation of the same phrase into colloquial English.
"It is nothing" usually shortened to "It's nothıng" thus using the Turkish phrase's present tense... would mean you are or will be doing something for them at the time they are saying "Thank you for doing this for me".
Its OK... but as a general courtesy in this instance ıt would be better to say "No problem!" or "Not a problem" (Its not a problem for you to do it for them) So "Problem değil"
Therefore both present tense and past tense English answers should be correct.