This effect is well observed in Firefox.

Example with cursor in text fields when switching from Firefox window to some other window:

Steps to reproduce:
1. Open Firefox and some page with text field in it - for example translate.google.com
2. Open some other app - for example Dolphin.
3. Place two apps side-by-side.
4. Click on text field inside Firefox.
5. Pay attention to cursor blinking in this field and use Alt+Tab for switching into other app.

Expected result:
Cursor immediately disappears from text field in Firefox and focus goes to other app.

Actual result:
Cursor blinks two times inside text field in Firefox and then focus goes to other app.