"They went from here, but they did not go to school."
Translation:Mereka pergi dari sini, tapi mereka tidak ke sekolah.
Yes, tapi is short for tetapi. The only difference is that tapi is considered more colloquial and tetapi more formal (similar to "don't" and "do not").
So, your answer should be correct. :-)
Interestingly, it is marked correct in the same exercise (just in present tense): "They go from here, but they do not go to school". And it is also marked correct when you leave out the second pergi: "[...] tetapi mereka tidak ke sekolah)"...