'He went into the room, opening the door using a skeleton key.' Is the time-sequence correct? Is the ‘using’ clause showing method?

Firstly, ing-clauses may often be used either to describe something intrinsic about the statement in the main clause

('He communicated using a radio' = 'He communicated by radio') (restrictive)

or to tack on additional information

('He communicated, using a radio' = 'He communicated; he did this by radio') (non-restrictive).

But what sort of additional information may be added using ing-clauses? And are there any restrictions we should be aware of?

This 2015 post at Helping Writers become Authors.com – K M Weiland by Eliza Dee has very useful analysis of how ing-clauses are used (note the older 'phrasal' analysis is used) (amended):

... [There sometimes seems to be an implication] that, because it’s the present participle that’s involved, there’s somehow a requirement that the relationship the participial phrase indicates must be one of simultaneity.

The problem is, it just isn’t true. ... [T]his supposed rule is not now, nor has it ever been a feature of English grammar, descriptive or prescriptive or otherwise. I haven’t even been able to find any advice along these lines that’s older than a few years, nor any that appears in any reliable grammar, usage or linguistics text, and when I asked my editors’ groups about it last year, in search of the source of the bad advice, none of the members there even knew what I was talking about or had ever heard of such advice being given. One did, however, point me in the direction of a very dry but extremely relevant-to-this-discussion linguistics text, Free Adjuncts and Absolutes in English: Problems of control and interpretation, by Bernd Kortmann, from which I’m drawing a lot of what I’ll go on to say below.

There’s nothing whatsoever technically wrong in a sentence like

• Tying her shoe, Josie heads out of the house.

The fact that the two events cannot logically be simultaneous is not a problem. In fact, present participial phrases are what Kortmann describes as “semantically indeterminate”—that is, they can mean different things, in terms of the relationship between the phrase and what it modifies, depending on context. As Kortmann explains, such constructions are “unmarked for tense and mood. Constructions without a perfect-participial head also neutralize the aspectual distinction ‘imperfective/perfective (progressive/non-progressive)’”. That last bit means, in linguistics jargon, that present participial phrases not only don’t tell us tense, they don’t tell us whether an action was completed (unless the perfect participial, eg 'having done something', is used).

Moreover, “whether the relationship holding between these constructions and the matrix clause [that is, the clause modified by the participial phrase] is a temporal, causal, conditional, etc., or an adverbial one at all, needs to be determined for each individual instance”. So not only is simultaneity not required, but 'temporal' in general is only one type of relationship these constructions can indicate.

One such relationship is, indeed, [just a basic] Simultaneity, but there are numerous others, including:

• Anteriority ('Reaching into the drawer, he took out a knife.')

• Posteriority ('She left her apartment, slamming the door.') –Note that the placement of the participial phrase is what tends to distinguish anteriority from posteriority; compare “He sat down, crossing his legs” with “Crossing his legs, he sat down”–the latter is illogical because no logical relationship between the phrase and the matrix clause, temporal or otherwise, comes to mind

• Conditionality (this one’s a bit trickier to understand, but for example, in a sentence like, 'He was a terrible husband, putting it mildly', the idea of the modifier is something like 'if we are to put it mildly') [a comment clause: a pragmatic marker]

• Instrumentality ('Using the knife, he cut his meat.')

• Manner ('The little girl walked to school, skipping all the way there.')

• Accompanying circumstance ('She stood in the hallway, wearing a red dress'– this is superficially similar to simultaneity, but not the same, as you wouldn’t say “she stood there at the same time as she was wearing a red dress” – it wouldn’t be logical)

• Concessivity (meaning something like 'although', as in 'Knowing the consequences, she broke the rule anyway.')

• Causation ([Hammering the cliffs, the incessant waves finally brought down the famous sea-arch.])

• Result ('He ran very fast in the footrace, coming in second.')

• Purpose [/ reason (involving a logical course of action taken)] ('He slowed down, avoiding a person he didn’t want to run into.')

The examples above are my own [I've given a correct causative, EA], but all the semantic categories are from the Kortmann text. ... Of course, whether they’re stylistically preferable in a given context is a different question, and a much more subjective question....

This is a very useful breakdown of semantic usages of present-participial clauses. I've given it for a complete overview, though the example of the instrumentality usage is (apart from the fronting) a perfect match. So an adverbial showing instrumentality, not method.

A wise person once said: "You are well-spoken if you are understood."

For a normal reader, the line makes sense. It feels normal and allows the reader to move on, understanding completely.