Writing Mass Balance Equations
There is no such convention explicitly telling what comes out first.
Here, for a traditional formula of phosphoric(V) acid $\ce{H3PO4}$ writing a proton first serves only a didactic purpose.
It's visually easier for students to keep a track on dissociation as the order of the elements both in formula and among the products is preserved.

On the other hand, shall one use a coordination formula of phosphoric(V) acid $\ce{[PO(OH)3]}$, it probably would make more sense to use a reversed order and put $\ce{H+}$ at the end:

$$
\begin{align}
\ce{[PO(OH)3] &amp;&lt;=&gt; [PO2(OH)2]- + H+}\\
\ce{[PO2(OH)2]- &amp;&lt;=&gt; [PO3(OH)]^2- + H+}\\
\ce{[PO3(OH)]^2- &amp;&lt;=&gt; [PO4]^{3-} + H+}
\end{align}
$$

One more minor thing.
Equations are usually aligned about arrows, and a tabular array of products and reactants emerges when the same repeating compound ($\ce{H+}$) is shown first.
Note how easier it is to grasp the information when more compounds are aligned:

$$
\begin{align}
&amp;\color{green}{\text{aligned}} &amp; &amp;\color{red}{\text{misaligned}}\\
\ce{H3PO4 &amp;&lt;=&gt; H+ + H_2PO4^{-}(aq)} &amp;\quad \ce{H3PO4 &amp;&lt;=&gt; H_2PO4^{-}(aq) + H+} \\
\ce{H2PO4- &amp;&lt;=&gt;H+ + HPO4^{2-}(aq)} &amp;\quad \ce{H2PO4- &amp;&lt;=&gt; HPO4^{2-}(aq) + H+} \\
\ce{HPO4^2- &amp;&lt;=&gt; H+ + PO4^{3-}(aq)} &amp;\quad \ce{HPO4^2- &amp;&lt;=&gt; PO4^{3-}(aq) + H+}
\end{align}
$$