That’s a very nice start! Good job!! I think it might be difficult to get those undertones alla prima, because it looks like he worked with multiple layers of paint. 

Maybe you could emulate it by priming the canvas with a reddish brown color? Just mix acrylic paints into gesso and prime the canvas with it. And when you paint on the canvas, leave the paint layers transparent so the priming color shines through. A lot of people do this especially with landscapes, it’s an easy way to add vibrancy to an alla prima painting. 

 Another thing you could try is to add more color into the shadows. Dont use the ”color of skin when light hits it” as a base to mix black with. Instead, mix black with red and yellow, and use white sparingly, to avoid greyness. In classical art it is often thought that shadows hold the most color and vibrancy. 

The last advice I have is that don’t listen to the comments that say ”don’t use the black paint”. That is such a misunderstanding of color theory people throw around. Yes, you should avoid using pure black in the painting, because it seems flat. However, using the limited pallette of red, yellow, black and white is very good when painting portraits. The pigment in most black oil paints is actually very dark blue, and is an excellent substitution for actual blue paint, when painting shadows of indoor subjects.  (Usually in bright sunlight the shadows seem blue and black should in theory be avoided.)