Does in review mean an external reviewer is assigned ? Three weeks ago, I have submitted a paper to a journal that has a reputation for fast publication process. On their website, they mention that decision on acceptance or otherwise are taken quickly normally within a month of receipt of the paper. One week after submission the status of the paper changed from waiting assignment to in review .  The journal use OJS for submissions. in review page something like this appear:

Peer Review
Round 1

Review Version    Final version.pdf  2018-11-24

Initiated    —

Last modified    —

Uploaded file    None

Does that mean still no external reviewer is assigned to the paper? Giving the circumstances is it too early to ask if any reviewer is assigned?
'Under Review/In Review' can mean that your manuscript is currently assessed or 'under review' by the assigned editor. This could be very likely, since you mentioned the status changed straight from 'waiting for assignment' to 'in review'. During this time your manuscript could be checked for formatting guidelines, the editor might judge the article himself or he might be in the process of trying to find suitable reviewers. For details on the different status messages of journal's workflows, here's a great answer.

Especially around holidays it might additionally be hard to find reviewers, and get back their scores within a certain time period. Also, even if a journal claims to normally take one month until the first decision, I suspect these times can have a big variance.

I suggest to wait until the holiday season has passed, and then follow up if the status has not changed yet.