If you open the doors on the side of the dryer, the air coming out is very wet.
Well you're blowing the air through a wet rug, what do you expect?
In-fact, it probably is not really all that wet. Doubtful that it is much above 40% RH at 150C. It feels wet when you open the doors and mixes with room air because the mixture will be quite high RH.
Simplistically, drying is driven by the difference in vapor pressure between the moisture in the product and the air.
If you want to determine if the air is picking up all the moisture it can, you'll need to look at the relative humidity - that being the amount of moisture in the air relative to the maximum that the air can possibly hold.
But...
Doing things to increase the RH on the air-leaving side of the web will result in only relatively small gains in moisture removal. The reason is that each pound of air really doesn't hold that much water.
More air is probably what you need.
Is the drier zoned? Cool dry air blowing through warm wet product removes more moisture than hot dry air blowing through warm wet product.
There have been a few threads here on drying - use the Google search facility at the top of the page.