Not all coins will be rising if bull run happens. Those coins at times are worthless and will never rise inspite if btc reaches 15k levels.
Only coins/tokens with real use-case will rise. Also, alt bull run won't happen if btc start rally for new ATH. Mainly alt bull run start just after btc stop the rally or stable at a price zone.
historically, altcoin season came when new ath was achieved by bitcoin and btc dominance decreased,
and it is true what is said about the price must be stable, if btc experiences a bearish trend then altcoin season can fail,
and a good plan for bullish season is to buy Altcoin hidden gem.