Ok, so I jump into my space ship and fly away at 75% of the speed of light, then after 5 years on Earth, I turn around and fly back at the same speed. To the people on Earth, I was gone for 10 years, but to me it was less than 10 years, and I aged less than 10 years (I don't think that general relativity is as simple as special relativity, so I don't think that I can calculate how long it'd be exactly)... So if, somehow, I fly away at 99% of the speed of light, then come back, I'll have aged barely, while Earth will have aged immensely; thus, I will have time travelled into the future..
As long as Crono and co. experience some aging while going into a future time gate, which is obvious because it shows them in the gates, I think, the situation is the same.
So Magus goes from 600AD to 12,000BC. Janus is altered due to Magus' presence, and becomes Janus', but Janus' goes through a gate to 600AD just as Janus would have done. A future time gate is like moving at the speed of light and moving back (I don't know the specifics of general relativity, but I think that aging less requires acceleration to a high speed and acceleration to a stop). In the original timeline Janus merely aged at an incredibly slower pace than his surroundings, nothing more. Magus' presence in 12,000BC rewrites the slowed aging of Janus, and replaces it with the slowed aging of Janus', so why would Janus result of Janus's (Janus prime's) slowed aging?