This situation does not fall under the definition of a "rush." A rush is an attack on an opponent's hero with reinforcements. Reinforcements are troops that were acquired at the beginning of the first day (for example, when transitioning from day 127 to day 131). Troops acquired after the construction of a building are not reinforcements; they are troops that come "as a package" with the building. Therefore, there is no violation of the rules in this situation.

Added 3 minutes later

Yes, according to the rules, that's how it is, but in reality, it's absurd, because there is no difference between reinforcements that appear at the beginning of the turn and troops built on the first day.

There is a difference, and it is significant. Money and resources were spent on the construction, so it is perfectly logical that the units can be used.