Role of acetate ion in formation of hydrogen sulfide ion from thioacetamide
You are correct.

Adding sodium acetate to an acidic solution forms a buffer and thus decreases the acidity of the solution without making it basic.

$$\ce{CH3COO- + H3O+ &lt;=&gt; CH3COOH + H2O}$$ 

This helps to precipitate sulfides $\ce{S^{2-}}$ without forming basic precipitates like hydroxides that might disturb the analysis.

$$\ce{S^{2-} + H3O+ &lt;=&gt; HS- + H2O}$$ 
$$\ce{HS- + H3O+ &lt;=&gt; H2S + H2O}$$ 

Heating the test tube just speeds up the hydrolysis of thioacetamide. To keep $\ce{H2S}$ in the system this is sometimes done in a hermetically sealed glass tube.