Skybox is correct. Folks on the NBIB/DCSA contract as of last year have their access / eligibility stored in JPAS and can take their eligibility to most jobs requiring TS clearance. I know a handful of people who have done this myself.
(To clarify, clearances / eligibility were previously stored in CVS but were shifted over last year sometime or so)
Being favorably adjudicated doesnât mean you have an actual clearance. I just got a real one last year; no idea why now after many years of doing job. But glad to haveâŚ
Whether or not you have an actual clearance is irrelevant - if youâre moving directly from the DCSA contract to a job that requires a DoD T5 investigation, they should be able to just flip the switch and activate you.
This literally just happened to me when I left the BI industry.
Couldnât have phrased it better myself. 
Your clearance eligibilty can be used by as many agencies as need it. Ever agency is a different drop down box in JPAS and every agency grants you access under their sponsorship.