I have noticed in a word like sense, the 〈s〉 is pronounced not like a fricative but as the affricate [t͡s] because it is followed by the nasal consonant /n/.
Is this phenomenon (a fricative turning to an affricate when it follows a nasal consonant) true, and if so why?
This phenomenon is indeed quite common, and it makes sense if you think about it in articulatory terms.
Let's take the sequence /ns/. For most speakers, [n] and [s] are quite similar, if not the same, in terms of their place of articulation. But they differ in terms of manner and voicing. The nasal [n] is produced with a full oral closure, an open nasal passage, and voicing, while the fricative [s] is produced with only a partial oral closure, a closed nasal passage, and no voicing.
In order to transition from an [n] to an [s], three things must happen: (1) The front of the tongue must re-position itself a bit in order to release some air out of the mouth, (2) The velum must raise to block air from escaping through the nose, and (3) The glottis needs to open to allow the passage of air without the oscillation of the vocal folds.
If all three of these independent articulatory actions happen simultaneously, the [n] transitions into an [s] without any intermediate output. However, if (2) and (3) happen slightly before (1), there is a short period of time when voicing has ceased and air is not escaping through the nose or the mouth, with the oral closure being that of the [n], i.e. alveolar. What is the resulting speech segment? The voiceless alveolar stop, [t]! Once (1) kicks in the air gets released and the [t] "gives way" to the fricative [s].
Incidentally, whether we decide to call the resulting [ts] sequence a stop-fricative sequence or an affricate is in some sense academic, since the [t] is really just the result of the [n] and the [s] overlapping articulatorily. (Wow, try to say that last sentence three times fast without any epenthetic [t]s!)
This is a form of epenthesis. It is quite common, but not universal, and varies both between speakers and with other factors, such as how quickly they are speaking. Whether it appears of not depends on the fine detail of the timing of the different articulatory actions: whether the glottis closes a moment before, a moment after, or at the same time as the tongue leaves the alveolus.
As you say, there is often a 't' audible in the sequence /ns/, and sometimes a 'p' in /mf/ (as in "triumph"); but I don't think a stop often appears in the sequences /nz/ (eg "men's"), or /nθ/ (eg "anthem").
