It is questionable whether there is such a thing as "assimilation of manner" in the same sense that there is assimilation of place. Assimilation of place traditionally refers to wholesale shift in POA as represented in the IPA charts, to t → p, p → k and so on: columns of cells identify a "place". "Manner" cross-classifies rows including nasality, continuance, sonorance and other features. An assimilation of manner would be where t → θ before all fricatives, → n before all nasals, and so on, likewise changes of p, d, z (→ d before all stops, → dz before all affricates). A language can certainly have partial assimilation of one feature: the question is whether there is ever a case of assimilation of all manner features?
The examples ts → ss, dn → nn are not clear cases, in fact they are completely ambiguous in that they could simply be total assimilation (all features). Typological research has revealed ample evidence for cases of place assimilation, and laryngeal assimilation, as well as total assimilation, and no evidence for manner assimilation. This is the foundation of the conclusion that "manner" is not actually a constituent in phonological feature structure.
Since there is no such thing as general manner assimilation in languages (distinct from single-feature "nasalization" e.g.), you'd have to understand the concept in hypothetical terms. For example, the following collection of changes:
{p → ɸ / _{s,ɸ,ɣ}
θ → t̪ / _{p,b,k,q,ɗ}
s → n / _{m,n,ŋ},
t → ts / _{pf,t̪θ,ts,kx,qχ}}
If you encounter something like that, you have found assimilation of manner. If you find complete assimilation, that is simply the extension of assimilation of place and laryngeal features to cover all features, and thus not specifically "assimilation of manner".