Your corks are probably turning red because wine has gotten between the cork and the sides of the bottle neck. This happens because when you force a cork into a bottle, the air between the cork and the wine gets compressed.
If you leave the bottle standing upright for 2-3 days, the pressure will work its way out around the cork. If, on the other hand, you lay the bottle down immediately, the pressure pushes the wine (instead of the compressed air) out around the cork.
Leave your bottles upright 2-3 days, then lay them on their sides and watch them for a few days thereafter. The bottles should not leak. If they do, pull the corks and put in new ones.
Make sure your corks are the correct size for a good fit.