There are three things to point out about this discussion:
1. The "material" concept of time. Time here is not intended as an abstract entity, a chronological coordinate, as we are used to.  A "time" is the complex of all existing beings, things, circumstances and processes occurring in a particular historical instant. So it 's like an enormous set including everything existing or going on at that moment. If you consider the next instant, another enormous set is determined and that 's different form the previous one, as many things or situations have been changed. So we are included in the times because we are among the countless things and beings "contained" in the flowing times.

2. Sorry Memoro, but I must notice that your feeling of a possible deponent behaviour of the verb "muto" is baseless and factually incorrect.
Indeed, consulting several Latin grammars and dictionaries I found no trace, no hint of a use of "muto" as a deponent or semi-deponent verb, at least in the classics. Simply, when a verb is provided with both forms, active and passive, it cannot be a deponent.
It is however true that "mutare", as well as "to change" in English, may have a transitive or intransitive meaning. When it is transitive there is someone who performs changing and someone who undergoes it; so we can use the active or passive form to determine who 's the agent. We can say  "I change you" or "I am changed by you", leaving no doubt on who 's the author and who the object of changing. In the second case (the passive one) it 's wholly evident that change is not due to my will.
With the intransitive meaning instead, the concept of voluntariness of change remains more shaded and vague. When I say: "I change", I make quite clear that some changing is affecting myself, but nothing is said about whether this change is due to my will or to the events, circumstances or somebody else 's will. Thus, using the active form with intransitive meaning, we can leave an open door to both possibilities:  - a. I am changing because I actually want to, or - b. I am forced to change by circumstances or others.
Therefore, whoever was the author of this maxim, he had a simple way to let us think that we might be the artificers of our own change. He only had to write the verb in its active form: "mutamus". A simple "s" instead of an "r". That wouldn 't even afffect the hexameter 's rhythm. But he (purposedly in my opinion) chose the passive form; so expressly underlining our "passivity to the change".
Moreover, he used a special trick to give an even stronger emphasis to the passivity. Normally speaking in Latin, one would say "et nos mutamur"; but here we see "nos et mutamur". Exchanging the pronoun with the conjunction is a rare expedient to emphasize the latter (in Latin language, everything that comes "after" has higher importance in a sentence 's  context). This special exchange serves to point out that this "nos et" is not a simple "et nos"; we should translate it as "and we too"; but other stronger translations could be: "and we forcedly", "and we ineluctably", "and we a fortiori". 
All this drives me to the conclusion that the sentence 's author wanted to stress as much strongly as possible that we are "passive" poor things in front of the general changing going on through the entire universe. So the true extensive meaning of the phrase is:
"When everything existing in the universe is subject to change by circumstances and force majeure; how could we, poor little human things, pretend not being changed as well?"
This way of reasoning comes quite natural if you "think in Latin".

3. According to the ancient and medieval way of thinking, this sentence is nothing else than an Aristotelian categorical syllogism; i.e. the basic unit of logical reasoning.
Here we have:
- a major premise: "Tempora mutantur"
- a minor premise: "in illis" saying that we humans are included in times 
- a conclusion: "nos et mutamur".
That simply means we are forced to change because we are part of all things that are changed.
In mathematical logic and set theory, these relations concern set inclusion. So here are: 
a set H containing all humans; a set T containing all times (as defined above) and an even bigger set C containg all things, beings, situations, processes, and complexes af all them, that are subject to changing.
The minor premise states that H is included in T, the major premise says T is included in C and the conclusion is H is included in C.
In other words this is what 's usually defined as "the transitive property of inclusion". Thus, a synthetic translation of our sentence in sheer mathematical terms is:   H ⊂ T, T ⊂ C   ⇒  H ⊂ C