Let $(M^{2n},J)$ be a complex $n$-manifold and $u:\mathbb{CP}^1\to M$ an immersed $J$-holomorphic curve. Then there exists a short exact sequence of vector bundles $$0\to T\mathbb{CP}^1\to u^{\ast}TM\to N_u\to 0$$ which defines the normal bundle $N_u$ of $u$. By Grothendieck's theorem, $$N_u=\bigoplus_{i=1}^{n-1}\mathcal{O}_{\mathbb{CP}^1}(a_i)$$ where $$\sum_{i=1}^{n-1}a_i=c_1(u^{\ast}TM)-2. \qquad \qquad\qquad (\star)$$
Question: Suppose $v:\mathbb{CP}^1\to M$ is another $J$-holomorphic curve which is homotopic to $u$ and let $b_1,\dots,b_{n-1}$ be the defined by $$N_v=\bigoplus_{i=1}^{n-1}\mathcal{O}_{\mathbb{CP}^1}(b_i).$$ Is it true that $b_i=a_i$ for all $i=1,\dots,n-1$?
Comments: Note that the answer is "yes" in the case $n=2$, since then there is only one unknown $a_1$ and $(\star)$ gives $a_1=c_1(u^{\ast}TM)-2$. I'n not sure if this is true in higher dimensions. Perhaps a counterexample can be constructed when $\pi_2(M)=0$ and all such curves are homotopic, e.g. $M=\mathbb{C}^3$. The question is essentially how the normal bundle can change within a given homotopy class.
It is not true. For instance, for lines on a smooth cubic threefold, generically the normal bundle is $O \oplus O$, but for some lines it is $O(1) \oplus O(-1)$.