Is it normal that doctor pressed down really hard on injection sites pretty hard after Botox (crow's feet and glabellar region)?

Yes this is a type of technique used. It has no negative effect on the result.  There are many studies that show this.  Best, Dr. Emer.

It is always possible any time a needle pierces the skin that there will be some bleeding or bruising associated with the procedure. If bleeding is noted immediately upon injection, the bleeding and bruising can be minimized by applying direct pressure to the area. This should be performed in such a manner as to avoid moving the Botox around and to avoid unnecessary pressure. Bleeding or bruising risk can be minimized by seeing an expert physician injector.

Bruising is a side effect of botox.  He may have pressed hard on the injection sites to minimize the bruising.  It is best to avoid any blood thinners like ibuprofen, alcohol and aspirin a few days prior to your treatment to minimize bruising.