There are no default tab stops for paragraph styles in FrameMaker; you need to set the paragraph stop(s) for each paragraph style, and then the Tab key will act as you expect.
You may find it easier to use the ruler bar to set tab stops when you are starting out. If you do, be sure to update the definition using the Paragraph Designer so that future and existing instances of that paragraph style will all have the tab stops.
I would not use a tab to align the pink line with the blue one. If for some reason you add more content to the pink line, then it will flow to a second line without an indent.
Tabbing at the beginning of a paragraph is typewriter style. I would indent the whole paragraph using the paragraph designer.