Alt-coin seasons tend to come in waves. In the last bull run we saw a bunch of alt-coins popping off before BTC did, for example XRP went from 0.4 cents (yes less than half a cent) to more than 40 cents in a matter of a few months. By the end of the year we saw BTC go to 20K and then XRP spiked soon after again.

SO it seems like they come at the beginning and then the end of BTC's bull run. IMO stock up on BTC now and then shift into alt-coins once BTC begins to lose momentum.