Yes, you are missing something. The generator displays the voltage **as if** put into a certain load. Typically a generator **assumes** 50 Ohm load and has an own source impedance of 50 Ohm. It compensates for that assumed load. If you connect a load with another impedance than 50 Ohm the generator gets its compensation wrong.

To deliver 1 Vpp into an assumed 50 Ohm load the generator has to put out 2 Vpp, because the generator's 50 Ohm impedance and the 50 Ohm load form a voltage divider 1:2. That 1:2 divider than divides the generator's 2 Vpp down to 1 Vpp, so the 50 Ohm load gets 1 Vpp. And everything is fine.

You are putting the signal into 1 MOhm. With the 1 MOhm oscilloscope impedance you have a voltage divider 1:1.00005, which is as good as 1:1 for practical purposes. But the generator still puts 2 Vpp into it, thinking it is driving a 50 Ohm load, and you get 2 Vpp.

Search in the generator menu for an option to change its output impedance. That option doesn't really change the output impedance, it remains 50 Ohm. But it changes what load impedance the generator assumes. If it knows it puts the signal into a 1 MOhm load it will assume a 1:1 divider, and just output 1 Vpp.