"tapa" is translated as "top", but more Americanized as "soundboard".
In Contreras' thinking, he was making a second "tapa", ie. thin piece of tone wood (usually cedar) minus bracing and adding it to the back (not bottom!) with the idea that it would reflect the sound and add tonal richness in a way that a solid structural piece of rosewood (back) can't.
This is different to the modern "double top" which is more accurately referred to as a "sandwich top" since it's actually a triple top.
Personally I believe that the contribution on the rigidity is that much that the dampening of the instrument is considerably less which leads to higher reflection and consequently to louder instruments.
The sound pattern of the instrument will change as well since some harmonics will be less dampened than the others leading to another tonal richness.
Greg Smallman was very aware of this property when he was building his lattice braced instruments.( back and sides multi-layer or laminated concept with large amounts of epoxy glue)
Epoxy sound ?
For sure not.
For double tops see also:
( site of Luthier Fritz Mueller referring to Owl’s reply)