Connecting micro-strip line and stub
You will often be able to get better results in simulation if you model something simpler than the real world. However, the purpose of using simulation is not to get good simulation results, but as a step to getting good real world results. That means modelling everything as faithfully as you can.

When you join transmission lines of different widths in the real world, there is a discontinuity, which is modelled by that 'Tee' piece that's upsetting your nice simulation results. 

The way ADS models lines is that they connect without discontinuity. That means the top picture you have there isn't finished. It's not a good model of anything. If you want a good model, you have to add the Tee. 

The reason that we add a Tee manually is that there are different models for Tees, some simple and inaccurate, some more complicated and better, or you might want to use a measure S-parameter file, and all depending on the physical construction of the lines. That's why ADS doesn't assume a discontinuity when you connect dissimilar lines. 

Why does it let you draw a circuit without them, like the top one? I don't know, I've never really thought about it, though I have often used ADS in a quick and dirty mode where it didn't matter so much, and I was allowing for the effects. Why shouldn't it let you simulate exactly what you draw? You alone know how well your real world is modeled.

If you leave it out of your simulation, and build what you think you've modeled, you're in for a disappointment.

How to dimension it? Look up the instructions for that component. You usually match line widths, but of course you need to specify them in the right order. You'll probably need an extra MLIN between your TERM and your MTEE.