Note: This topic has generated a fair amount of discussion for such a minor point. At the very least, I have been able to share some of my pain at dealing with these problems every day. Not, I hasten to add, that it is anything other than a delicious pain!
In any case, just to note that so far as I am concerned, the question was solved by @DKervick when he pointed out that MN 107 is set in Sāvatthī, so the sense “headed west” works in both cases. So I’m just keeping the following as a record of the discussion.
In a couple of places we find the idiom pacchāmukha, which has been translated as “facing west”. It occurs in MN 107, where a man is given instructions as to the road to Rājagaha, but takes the wrong path and “goes west”. It also occurs in Thag 10.1, where the monk Kāḷudāyin encourages the Buddha return home to the Sakyan republic, crossing the river Rohiṇī “facing west”.
Now, both of these contexts kind of make sense, but I have my doubts.
Firstly, there is a standard idiom for facing in a direction, and it uses abhimukha rather than just plain mukha. So far as I know, we don’t find mukha used this way with any other direction. But maybe it’s just an idiomatic variation.
Secondly, in MN 107 it’s not clear why heading west would be associated with someone losing their way. There’s nothing in the setting to indicate that they have any particular spatial relation to Rājagaha, so why introduce a specific direction here?
Finally, in Thag 10.1 they are said to be seen by the Sakyans and Koliyans as they cross the Rohiṇī. Now, as is well known, a story in the Buddhist tradition concerns the dispute between these two clans over the water from this river, which apparently formed a boundary between them. According to the background story, the Buddha is at Rājagaha, and it does make sense that he would cross the Rohiṇī heading west.
However, perhaps another meaning is intended: pacchā means “back, behind”, and mukha means “front”. In the context of the road to Rājagaha, this clearly makes better sense: he gets the instructions “back to front” and goes the wrong way.
In crossing the river, it is not so clear, but it could refer to the fact that the Sakyans and the Koliyans, on opposite sides of the river, see the Buddha crossing both “back and front”.