The Ready State Virtual Mobility Coach is like having a virtual Kelly Starrett in your pocket.
On days that I do a lot of overhead pressing, my right shoulder gets smoked fast and sometimes causes numbness and tingling down my whole arm.. Is this likely a technique issue?
Doubtful that it is solely technique, because it sounds like thoracic outlet syndrome. This means a number of structures could be compressing your brachial plexus when you reach overhead. Look it up in the search bar and try some of the mobs to see if they help.
Sounds like tight scalenes could be part of the problem. Type in “overhead” in the search bar there will be plenty of videos to refer to. First rib, tight triceps etc. All of these could be affecting your overhead position.