There are traces of it, yes, but by the time the 6 hours hold passed the solution has neutralize so it's safe to put the contact within your eye without doing anything. I do basically that every day and I've never have a problem.
The solution is there to hold your contacts from drying. It's actually best to enjoy your contacts a bit wet when putting them surrounded by so that they won't hurt when going in your eye.
The solution is neutralize after 6 hours, so it's harmless and wouldnt irritate your eyes at that point. If it worries you, you can bring back a bottle of saline (i prefer to rinse with it, anyway) and rinse your contacts past putting them on in the morning.
If you rub the contacts you may merely get grease on them before putting them contained by your eyes, which isnt ideal. I would speak rub them at night past you put them in the solution, and rinse next to saline before you put them on within the morning.
The answers post by the user, for information only, LasikAnswer.com does not guarantee the right and should not be considered medical counsel, diagnosis or treatment recommendations.