What the rest said! �� In the Airbus you may want to know that you are in ALT* because there could be a mode reversion to V/S until ALT is annunciated.
Tip: if you are not happy with the ALT* calculated capture of your altitude (entering ALT with changing dynamics, i.e. large +- speed trend and/or speedbrake retraction/extension, Engine fail, reduction to CLB thrust from TOGA/high flex subsequent to ALT* engagement) you can force an ALT* recomputation by pulling the ALT selector once again. This will recompute a new capture using a new snapshot of your aircraft state/energy, this could avoid unwanted speed excursions as a consequence of a a too steep/shallow capture geometry.

Do you know that for absolute certain? I’ve never heard that?

Yes I am certain.

Try it in a (high energy) go-around where ALT* will engage before Thrust reduction to CLB. You will find the Airbus sliding back on its tail struggling with the geometry of the altitude capture because of the thrust reduction after ALT*. Pulling the ALT again will force a re-computation.