Yes generally the training in a math degree is quite different from that of an engineering degree, in particular when it comes to practical stuff.
In many circumstances the language describing the background required of a candidate is a little less limiting than “engineering or physics” and will encourage applicants from cognate fields.
Of course mathematics is rather diverse in itself, and one can argue that training in more applied mathematics - theoretical signal analysis, control theory etc - should be considered as training in a cognate field. However, one can also appreciate that a student with a focus in number theory or algebraic topology might have to work harder to make a case. (For that matter, not every graduate in physics would be suitable for a graduate degree in engineering either...)
It seems to me the question is: do you really want to apply to a department that prima facie is implicitly suggesting you do not have the requirements of the program? Maybe the thing to do is to contact faculty members with research interests overlapping yours to ask if they would entertain supervising someone with your background?