Yes, they do fit. They fill the whole container but it fits and I've used the Tommee Tippee in it many times. It takes about 4 minutes to heat a 6oz bottle and there is no timer on it. I would say the lack of a timer is the biggest downfall. It will get too hot if you forget to take it out on time. Works fine other than that.
The lowest setting typically takes at least 10 mins to warm a cold bottle of 3oz formula. I typically use the lowest setting when to start warming the formula while I bath my baby. The good thing about this warmer is it goes off when the set temp has been reached abd starts off again if the water needs to be warmed to maintain the set temp. I have had it about a month and feel it is safe, but as with all appliances you can't be too careful so I always unplug when not in use, even though it has this self regulating feature to prevent overheating and such