Moyes is getting Everton to press high up the pitch. Its caught other teams out but a) we cant sustain that pace over 90 minutes and we've been pegged back twice because of it, and b) it wont take other teams long to figure out that's what Everton are doing and they'll by-pass midfield and the press and we'll be in trouble.
This upturn is all about short term effects.
Bottom line is staying up, as you said before Moyes took the job.
Mission completed.