The anxiety among some expats was brought about not by 'project fear', but by the stupid mishandling by Teresa May and her hapless team, none of whom have any past experience of real negotiation.
She stated straight away that all EU nationals in the UK would be allowed to remain as they are. The EU said nothing, except to itself "good, we'll have that".
The sensible way to have negotiated, was not to make a promise, but to have, at the outset, asked the question; "If we promise protection to your's, will you reciprocate with ours?" thereby making them come up with a statement and a commitment.