No, the way to define the reduction functions isn't related with the hash function used.
Let's consider that we want to recover a password $pwd$ knowing $hsh = H(pwd)$ where $H$ is a hash function. So we will compute a rainbow table for a certain set of passwords $\mathcal{P}$. Note that when the hash chains are computed, at each step $i$ we apply the hash function $H$ and a reduction function $R_i$ (note that several reduction functions are used to avoid collision problems).
A distinction must be made between the hash function $H$ and the reduction functions $R_i$. The reduction functions are used to map hash values produced by $H$ back into values in $\mathcal{P}$.
So the way to define the reduction functions $R_i$ depends on how you chose the set $\mathcal{P}$. For example $R$ can be the decomposition in base $n$ where $n$ is the size of $\mathcal{P}$ (the incrementation functions $R_i$ can be simply defined by incrementing the input of $i$ and then apply the decomposition).
The Wikipedia page also gives an example:
An example for a reduction function: Given a 32 bit hash, get the last
6 characters in the hash.
