Thanks for your reply! Really sorry for your cat, I lost mine for two days and know how it feels. Let us know if you find it!
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I read your answer and managed to specify and simplify a bit my situation:

I make a brand new environment. I make a grass.dmi with a 32x32 all green picture. Define it as a turf. Make a player.dmi for my player, just a 8x8 circle smiling face. Then a 7X 5Y map, make it full of grass. I use the code:



I test it and to my surprise the movement is exactly as I want, "tile movement" as you mention.
Then I make a flower.dmi, shows a 8x8 flower. Define it as object. So, now the last lines of code changes to:



Place just one of them on the map and test it. The movement changes to pixel movement, aka my player immediately appears onto the next tile.
Why is this behaviour so?

Edited: Ok, I expected I am noob but not this much. Guess I got much to learn! Changed obj step_size to 32 and works fine -_-

I tried to rig up custom gliding using animate() for games with pixel movement using high step sizes at low fps. But I couldn't quite figure it out. (step_size=16, fps=16, icon_size=32)