Use StackBlitz to reproduce your issue: https://stackblitz.com/edit/components-issue-wsbxpk
Steps to reproduce:

Selected tab is scrolled fully into view and righthand pagination button disabled just as if the user manually clicked on the last tab

Tab is only partially visible and pagination button remains enabled. When tab titles vary in size only a few pixels of the last tab are visible. Clicking on the last tab manually scrolls it fully into view.
Looks like we're measuring the element too early, because adding a timeout before skipping to the last tab fixes it.
Confirmed that this still happens in v9: https://stackblitz.com/edit/components-issue-1m6t8u?file=app/app.module.ts
Still happens in v10. Do we have any plan on this?
Use case: I have several tabs, and set the last tab as the default selected tab. After rendering the tabs, the selected last tab is partially shown.
Tested in v11, and it currently happens for the first tab when pagination is added. After that, it is correctly showing the tabs
https://stackblitz.com/edit/angular-mat-tabs-issue-uwcjql?file=src/app/tab-group-dynamic-example.html
But additionally, if the title is changed afterward, the position isn't recalculated.
Most helpful comment
Looks like we're measuring the element too early, because adding a timeout before skipping to the last tab fixes it.