Can I use a participial phrase in this way to modify the objects of a sentence?

I’ve been thinking recently about participial phrases and all the ways they can be used. I’ve been advised that it’s good to think of them as providing a supplementary predication about the subject, which I find a very useful way of looking at them. But when a participial phrase is offset by a comma, does it always have to be the subject of the sentence who is linked to it?

For instance, is there anything grammatically wrong with this sentence? Does it sound awkward at all?

• I asked Steve to tie one end of the rope around the tree, making sure the knot was as tight as he could make it, and then come and meet me on the bridge.

And similarly:

• As punishment, the teacher told Dan to walk around the whole school field, picking up any litter he found.

In both cases the participial phrases offset by commas aren’t linked to the subjects ("I" in the first and "the teacher" in the second) but to the objects. Is that acceptable, or is there any ambiguity?