Leaving the full sentence alone for a moment, the word "tomorrow" only refers to a particular day once supplied with a context (the day the word is spoken or considered).
So, if you assume that some context will be supplied at the time that "tomorrow is Monday" will be evaluated for truth, then in that context it will be either true or false. Then you'd say it's a proposition.
If you don't assume that some context will be available, then the phrase cannot even in principle be evaluated for truth. Then you'd refuse to accept it as a proposition.
As to how this would arise in practice, suppose you're given some mess of statements like "Tomorrow is Monday. Yesterday I saw a bus. All buses are red. I haven't seen anything red in 8 days", and asked to make some kind of sense out of them. If we assume that all the statements are evaluated on the same day then this seems contradictory, and on the face of it I appear to be lying to you (I mean, for starters, it's Monday today as I write this). But what if a week elapsed between the first statement and the last? Then I could have been telling the truth each time. I can say "Tomorrow is Monday. Tomorrow is Tuesday" and both statements be true, if the full stop between them happens exactly at midnight. The context completely changes how we evaluate them, and whether we can evaluate them at all.
So, whether we allow "Tomorrow is Monday" as a proposition depends on the context in which we're going to evaluate it (how are we going to account for changing time?), not on the simple definition of "a proposition". If we can make it into something that's either true or false then we can use it as a proposition. If we're stuck saying, "well, it depends when you say it" then perhaps we can't (or perhaps we can, but it remains a variable in whatever logical operations we do to it).
Many real-world statements involving "is" are liable to change, even if they don't explicitly mention time, but usually we reason about them anyway, having implicitly made some assumption that we're reasoning about a particular fixed moment in time where our assumptions are true. So we allow things like "the sky is blue", "I have three donuts" or "I think therefore I am", ignoring that none of these will be true forever. At any given time either it's true or it's not, and usually that's good enough.
The good news is that once this introductory stuff is out of the way, it won't actually matter whether "Tomorrow is Monday" is a proposition or not, because that's not the kind of statement you'll be reasoning about. Mathematics is not the study of what day it is ;-) We're on much safer ground with "0 is an integer" or "$f$ is a continuous function".
Tbh I think the question is unfair: you shouldn't be asked to guess for yourself whether "Tomorrow is Monday" will or won't be an acceptable proposition, without knowing what you're going to do with it.
At this introductory level the important point should be that a proposition can be considered either true or false for the purposes of the logic you're about to do. Whether it's "actually" true or false in all contexts goes way beyond simple propositional logic. Saying that because it's time- or reference-dependent it's not a proposition is a sort of "gotcha!" that the textbook might regret if the same standard were applied to its other examples of "real-world" propositions!
Another important observation to learn from is that you've got two sources who've defined "proposition" to their own satisfaction in pretty much exactly the same words, but they've made different unspoken assumptions that lead to different decisions whether "Tomorrow is Monday" is a proposition or not. The lessons to learn are:
- definitions can be insufficient to cover all cases, and it's better to write definitions that don't allow any such differences of interpretation. When you encounter unspoken assumptions, speak them, exactly as you did in saying, "depending upon the day on which it is told".
- people can disagree about definitions, and that's fine as long as you don't mix up conclusions reached using one version of a definition with conclusions reached using a different version. Where possible stick with the definitions and examples in your books, but bear in mind any variant definitions you encounter in other sources. Never assume that just because the same word is used for something in different sources, it must refer to the same definition!