No, it isn't automatic that a college player is ineligible because they played on a team with a professional. The influx of foreign talent pushed the issue. In basketball it goes back to the 90's that I know of, where a foreign player would come over to go to school ... those that could prove they got only expenses paid but didn't receive actual pay or any other monies were given NCAA eligibility. I'm not sure when that actually went down (could have been sooner) but that's what opened the flood gates.
OK, gotcha. You are talking about playing with professionals before you start college. I wasn't addressing that. The question was about while you are in college.
It differs depending on division: http://www.petersons.com/college-search/amateur-status-sports-college.aspx It was the "before" aspect that kicked it all of and forced the issue to be addressed.
From your link: That is what I was talking about and what the original question was asking. You cannot play with professionals during the period in which you are participating in college athletics.
You can't compete professionally ... not you can't compete on a team with a professional. Those aren't the same things.
The article also says: Which seems like a weird rule. I don't see why playing on the same team with a professional, or against professionals, should jeapordize one's amateur status.