In strong decays, the products will contain the same quarks and antiquarks that have existed in the original particle, possibly with the addition of one or more quark-antiquark pairs that have been generated during the decay.
In weak decays, one or more of the original quarks or antiquarks will be converted in a quark or antiquark with a different flavor, which is a process that has a low probability of happening, so the weak decays happen less frequently, therefore the hadrons that can decay only through weak decays have a lifetime that is many orders of magnitude greater than the hadrons that can decay through strong decays (or electromagnetic decays, i.e. annihilation of quarks with the corresponding antiquarks).
D+ is c quark + d antiquark, D0 is c quark + u antiquark
Tcc(3875)+ is 2 c quarks + d antiquark + u antiquark
Therefore the 4 quarks/antiquarks in Tcc(3875)+ are the same as the 4 quarks/antiquarks in D0 + D+.
So this is a strong decay, because no quark or antiquark is converted into another kind of quark or antiquark.
For the Tbb- tetraquark, its composition would allow a similar strong decay into two b-quark + u or d antiquark hadrons, except that its binding energy is so great that the mass of the Tbb- tetraquark is smaller than the sum of the masses of the hadrons that would be produced during a strong decay (it is also smaller than the sum of masses of the hadrons that could be produced by an electromagnetic decay, see
https://www.sciencedirect.com/science/article/pii/S037026931...
).
This forbids the strong decay and the electromagnetic decay, so the only admissible decay must be weak, where one of the b quarks will be converted into another kind of quark.