Kind of old question I guess, but I reckon there are more people with this problem.
I don't think there is a setting to open all programs on the primary display on Gnome.
But as a workaround you can enable workspaces only on the primary display, and make rules for all the programs you want to force to primary.
Start gnome-tweak-tool.
Workspaces -> Turn on "Workspaces only on primary display"
Extensions -> Turn on "Auto move windows"
Press the gear to enter settings, press "Add Rule", choose program and workspace number.
Make a rule for each program you want to display on primary.