"to phone in a [performance, for instance]” is to complete the performance but do the bare minimum, without enthusiasm.

Is this a fairly new usage (last 15 years, say)?

I have never noticed this.  In what context have you seen this term?  What sort of performance?  I am tempted to assume that this may refer to “phone” as in “telephone” but then it should be spelled “‘phone” --right?

Looks like it goes back to the 1930’s according to Ben Zimmer’s column:

http://www.visualthesaurus.com/cm/wordroutes/1578/

“The luxury afforded by the telephone of transmitting a message from a distance (rather than having to show up in person) led to all manner of jokes. Among stage actors, a “gag” circulated about an actor with a role so small that he could phone it in. A glimmer of this joke can be found in a February 1938 syndicated newspaper column called “Senator Soaper Says.” (Senator Soaper was a pseudonym for Harry V. Wade of the Detroit News.) The column includes a sarcastic comment about Thornton Wilder’s Our Town, which was then a new and controversial play. As our own Shannon Reed recently explained, Wilder explicitly laid out the stage instructions for the play: “No curtain. No scenery.” “Now that a Broadway drama has attained hit proportions with no scenery,” wrote Senator Soaper, “the next step is to have the actors phone it in.”

I am tempted to assume that this may refer to “phone” as in “telephone” but then it should be spelled “‘phone” --right?

Are you joking?  It’s been decades since I’ve seen anyone bother to use an apostrophe when shortening telephone to phone.

I think the passage quoted by jtab is using the phrase literally, although it arguably anticipates the pejorative metaphorical sense OP asks about.

No, I was serious.  I thought it may have come from a source [edit: like a dictionary] that respects [edit: or observes the convention of indicating] the forms such as when indicating a suffix like ”osity” it would rather be ”-osity” --in everyday writing I wouldn’t expect to see it.

But phone isn’t a suffix, either as a verb or a noun. It has been used as a freestanding word for more than a century; the OED has as many citations for it without an apostrophe as with one as early as the 1890s. And it hasn’t been normal to use the apostrophe for half a century at least.

Well, I stand corrected.  I have to admit I got trapped somehow early on because I have always thought that “‘phone” was more exact than “phone.” Maybe a time warp?  Nah.  Just something I always thought now turns out to be not so.

I’ve never, ever ... EVER ... seen an apostrophe on phone.

I’ve seen one on cello and that’s bad enough.

Thanks greatly, jtab4994, that’s amazing!

Just something I always thought now turns out to be not so.

That’s one of the side effects of hanging out around these parts!

I’ve never, ever ... EVER ... seen an apostrophe on phone.

I have seen it but rarely. There is one citation in the online OED from 1886: ”California Maverick (San Francisco) 13 Feb. 1/3 To him I related the famous fiend’s new invention—this ‘phone that could talk in foreign languages.”