Partial truth...

it is best to wait until the new season starts, then renew. The salary will be the same, but the signing bonus will be about 10% less. Renew on Day 1 of new season, not day 28 of previous season.

Just make sure you have 14 players under contract for the start of day 1. If not, you will get old, retiring players to bring you up to 14 players with contracts.