Naw, it's not a problem. Observe! (waves hand)
Appearing in deep space has a couple of problems. First, it assumes an absolute reference frame, which Einstein assures us doesn't exist. Second, moving from deep in Earth's gravity well to deep space would required the same amount of energy as launching from the Earth to deep space. So it ain't gonna happen.
Instead, in the absence of an absolute frame, time travel occurs within the local frame, which is defined by constant gravitational potential. In other words, the Earth drags local time along with it, so you'll always end up on Earth. Also, angular momentum figures into it, so you'll also always end up on the same *part* of Earth.
(stops waving hand)
This example of handwavium brought to you by that Martian guy who wants to disintegrate things.