돼요 is not the "more" correct conjugation of 되다. It is nothing but a contraction of 되어.
So in your question, the verb 돼요 is correct. But if you are writing a different expression - say, 될 수 있다 - then 되 is correct.
I ran the following sentence in Google translate, and this is what I got:
I became a pig.
나는 돼지가 되었다.
Notice that, while Google uses the 되 form, you can actually contract 되었다 to 됐다. The latter is preferred.
My guess is that Google decided to leave out unnecessary contractions to lessen the complexity of the algorithm behind the translator. It would be great if someone who knows the real reason can shed light on the topic.
Likewise. If we were to "expand" 돼요, we'd have to write 되어요, not 되요. If this is precisely what your phone is doing (돼요 -> 되요, verbatim), then I'm not really sure why.