Let me take a moment to explain, briefly, how tactile paving works,

This is a warning ripple. The purpose is to alert a blind person of something. You can find these usually on street crossings where the sidewalk is on level with the street, so blind people have a hard time detecting them. They can also be on top of stairs.
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This is a directional block (or rather several of them). The purpose is to lead to/away from something. You would typically tag these on the way where they are, so the ways leading to / away from the stairs. Most of the time, they lead to/from a warning ripple, so blind people are guided to / away from something.
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I’ve worked with blind people extensively 25 years ago. To them, just having a warning ripple on the top of some stairs would be considered having tactile paving, because you typically don’t put them at the bottom.

So, personally, I wouldn’t tag tactile paving only on the top of the stairs as partial or even incorrect, if the only intention is to warn people about the danger of stairs ahead. Strictly speaking, only the warning ripples should be tagged on the stairs, the guiding lines should go to the way leading to/from the stairs.

If the blue area on this pic were steps (it’s a ramp, I couldn’t find outdoor steps), then I would tag it like this: