= Solution
Write the alkyne as $\mathrm{Mes_2P-C_\alpha\equiv C_\beta-Ph}$. The product places Al at $C_\alpha$ and H at $C_\beta$:
$$
\boxed{\mathrm{Mes_2P-C_\alpha[Al(tBu)_2]=C_\beta(H)-Ph}.}
$$
A useful <Lewis acid>-assisted model begins with a side-on or bridged alkyne–Al interaction. As in the unsymmetrical bonding of aryl-bridged aluminium aggregates, the electrophilic Al center can interact with more than one carbon while a donating group biases the contact. The phosphine can additionally associate transiently with Al, organizing the alkyne near an Al–H bond. Transfer of hydride to the distal carbon while the proximal carbon retains Al gives the observed regiochemistry.
The drawing requires \b[syn addition of H and Al]. In the printed alkene, $\mathrm{Mes_2P}$ and Ph are opposite; consequently Al and the newly added H are on the same side. A cyclic <hydroalumination> transition state produces this relationship. Steric congestion subsequently inhibits a persistent P$\to$Al bond, leaving the two sites available as a <frustrated Lewis pair>. A long-lived free vinyl cation or an anti hydride attack is unnecessary, and would not naturally explain the <stereochemistry>.
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