If you attack a champion standing under a tower, the tower will instantly start attacking you. Please note that damage is counted not only from basic attacks or skills. Even if you deal damage with the help of some auras or objects, the tower will also begin to attack you immediately. Practice on smurf accounts from happysmurf.com.
If you use skills that, for example, slow down the enemy but do not damage him, then the tower will not react to this. If you simply break the tower and do not force a fight, then the tower attacks enemies in strict sequence, that is, the tower has priority targets. Below is a list of priority targets for the tower and the order in which the tower attacks them.
Various active items and traps (for example Jack In The Box)
Summoned creatures (for example Summon bear: Tibbers)
Siege Minions and Super Minions
As you can see, the tower attacks the champions at the very last moment. Therefore, if there are no enemies nearby, then under the cover of your minions you can cause damage to the tower for a very long time and quickly destroy it.