Red Hulk is Thaddeus Ross, or in this case President Ross. Father of Betty Ross, Bruce Banners main love interest. Ross is also somenoe who has been hunting Banner/The Hulk for…well…since the Hulk became the Hulk. Red Hulk was created as part of a Super Soldier Program (ala Captain America) with the aid of Doc Samson and the organization known as Intelligencia which is headed up by The Leader and MODOK (Leader is in this movie). Ross became The Red Hulk in order to deal with Bruce Banner and to yet again try to establish new Super Soldiers which has been a long time running thing in the Marvel Universe because of what happend in WW2. Red Hulk, Wolverine, Deadpool, etc, etc, etc are all different versions of a Super Soldier program (In Canada called the Weapon program).

So having Red Hulk in a Captain America movie just makes sense. Also would help with introducing the upcoming Thunderbolts movie as Red Hulk/Ross is also involved with that team. Could also tie in with Deadpool as they were both in the Thunderbolts.