Why are Oracle call instances bounded in the definition of FPT Turing reductions?
As Pål GD mentions, the requirement that $l(y)\leq g(k(x))$ is necessary to obtain reductions with the proper result. In particular, the property 'If $X$ is FPT, and there is an FPT-reduction from $Y$ to $X$ then $Y$ is FPT'. 

An example to see why this requirement is necessary is to consider reductions between $k$-Clique and $k$-Vertex cover. Recall that we can construct polynomial time reductions both ways between Clique and Vertex cover (without the parameters), using the fact that if $X\subseteq V$ is a maximum clique in the graph $G$, then $V\setminus X$ is a minimum vertex cover in the complement of $G$. 

However, this doesn't give a FPT reduction from $k$-clique to vertex cover: If we try to solve $k$-clique by finding a vertex cover in the complement of $G$, we need to find one of size $k'=|V|-k$. As $k$-vertex cover is FPT, applying the reduction and solving $k$-vertex cover can be done in $O(f(k')\cdot|G|^{O(1)})= O(f(|V|-k)\cdot|G^{O(1)}|)$. So, we don't get an FPT algorithm for $k$-clique from this 'reduction', as the 'non-polynomial' part of the running time depends on $|V|$! In fact, we shouldn't expect $k$-clique to have an FPT reduction to $k$-vertex cover, as $k$-vertex cover is FPT, but $k$-clique is $W[1]$-hard.



Additionally, I agree with Pål GD that the definition of parameterized Turing reductions you give is a bit difficult to read. I've looked at Flum &amp; Grohe's book and their presentation of this definition is in fact a lot clearer than than one you provide (from a different book/edition?):


  Definition 2.8. Let $(Q,\kappa)$ and $(Q' ,\kappa' )$ be parameterized problems over the alphabets $Σ$ and $Σ'$, respectively. An fpt Turing reduction from $(Q,\kappa)$ to $(Q' ,\kappa' )$ is an algorithm $\mathbb{A}$ with an oracle to $Q'$ such that:
  
  
  $\mathbb{A}$ decides $(Q,\kappa)$.
  $\mathbb{A}$ is an fpt-algorithm, that is, there is a computable function $f : \mathbb{N} \rightarrow \mathbb{N}$
  and a polynomial $p(X)$ such that the running time of $\mathbb{A}$ on input $x \in \Sigma^*$ is bounded by $f(\kappa(x))\cdot p(|x|)$.
  There is a computable function $g : \mathbb{N} \rightarrow \mathbb{N}$ such that for all oracle queries
  “$y \in Q'$?” posed by $\mathbb{A}$ on input $x$ we have $κ'(y) \leq g(κ(x))$.