Not an expert but reload a lot of .38 Spec - I think any non-magnum small pistol primer is fine. RD is a fast-ish burning powder so I sure wouldn't use magnum primers. Hornady 9th does not list Red Dot for .38S so I can't comment on the 3.4-g. I use Power Pistol and Universal for mine.

Edited to add - you've prolly already done your homework on this but your 3.4-g Red Dot is right on the money for a +P starting load for 158-g bullets per Speer ...

https://www.speer-ammo.com/downloads...cial_P_158.pdf