Carboy Rubber Stopper Problem?

I went to put the rubber stopper in my new 6.5g carboy last night, but it felt like it was squishing itself back out of the carboy opening. With the airlock in the rubber stopper it was even worse! I had the feeling that if I left it like that, the slightest pressure build up would push the whole rubber stopper right out of the carboy neck; so i shoved a large sanitized hose down the carboy's throat instead

1) Are those rubber stoppers supposed to fit in the carboy necks like this?

2) Should the rubber stopper be dry?

3) Should the inside of the neck of the carboy be dry as well?

5gB

Dry it off and do the same to the neck of the carboy. I have that problem every once in a while too. I think it's the non-universal bungs

I dry mine off with a paper towel...which some around here say is sterile... ...no problems encountered so far.