What altcoins season normally means is that, Bitcoin growth slows down, stops or starts dropping then altcoins are left with more room to grow, but it is very good to know that, the more Bitcoin dominance drops the more altcoins have enough opportunity to grow and the more intense the altcoin season will be.
They grew in price because, some funds which were initially being invested on Bitcoin are being moved towards altcoins, this is why you will experience a drop in Bitcoin price and an increase in altcoins price.
And lastly, the easiest way to determine if an altcoin season has started is, when the market turns green and many altcoins starts growing massively with many experiencing a good increase from their initial price to many also approaching or crossing their All Time High.