Are you changing the stock in the old tank(s)?
Where are the fish your adding to the new tank coming from?
If you are moving fish from the mature tank to the new tank, then the mature tanks bio load is decreasing and it can handle a loss of bacteria with no ill effects…
If the fish going into the new tank are new fish and the mature tank’s stock is the same, then you should expect spikes in both tanks as you now need more bacteria than you have…
If the new fish have been received through the mail they are probably quite stressed and have been starved for a couple of days already. So giving them the best conditions including food is important. If they were bought locally the transportation was far less stressful and they have not be starved…
And I still stand by the opinion that using old tank water is only beneficial as a way to keep consistent water parameters when moving fish from one tank to another and using fresh water is better for the new fish in the new tank…