Prepare for the short window
Alphas are larger and tougher than ordinary enemies. The capture window lasts only a few seconds, so get close in advance if you want the support.
Support or immediate rewards?
You can carry 2 support Alphas by default, or 3 with the Lab upgrade. Recruit for help with damage, or consider release rewards when your support team is sufficient.
Overlords and Summoners are minibosses that drop incense and blessings; they are not the same as recruitable support Alphas.