I'm a new member here and will soon write about my experience, but some of my experience overlaps with yours.   

My opinion: I am betting that your application or pre-poly booklet for the agency that you passed asked about other agencies that you've applied to.  If you put down the agency that DQ'd you, they may find out if your background investigator looks into it and contacts that agency... which my guess is that he will (I know I would if I was a BI).   

If you didn't disclose that, or they didn't ask about other agencies for some reason, you'll probably be good to go.  Unless the other agency ran your criminal record as a precautionary thing, and that check is recorded.  In which case a good BI may put two and two together and go ahead and contact that agency anyway.  It depends on your BI and how proactive he is.

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They probably wouldn't DQ you based on another agency's results,  but it may raise a red flag which could prompt more digging.   

It's not necessarily that you failed the first poly.  It's that you made admissions in your first agency exam... then in your second,  you didn't admit to these things.  So the BI may dig,  talk to the other agency about what you admitted, and discover these discrepancies, which may be looked at as you being deceptive. If the second agency thinks you're lying to them or covering something up,  you're probably done.  You may not get an official DQ but chances of selection are slim. 

From my experience, they do not care enough to look at BIs or polys you took from other organizations.  I passed three for other orgs and the CBP polygrapher still decided that he was right and I was lying.