It looks to me like one needs to use "Target Intersects Universe" of the Spatial Match tool in order to identify zip codes in a larger geographic space (Place, DMA, CBSA, etc.), and not "Target Contains Universe" or "Target Within Universe".
The Raleigh "Place" from the Allocate Input tool is an Incorporated Place (thanks, Mandy Gray @mandycgray) according to the Census. Allocate indicates its Key value as 37550000 (a concatenation of the place’s State FIPS + Place FIPS) and that is "Raleigh City" according to https://www2.census.gov/programs-surveys/popest/geographies/2019/all-geocodes-v2019.xlsx. The Place FIPS is not "00000" for "Incorporated Places".
I think the spaces within the Place boundaries causes only "Intersects" to work (compare Raleigh_Place.png to Zip_27612.png - both from the Browse tool). This is probably only true for some Places.
One can see the results of the attached Spatial_Match_InsersectNeeded.yxmd for an example using Raleigh, NC zip code 27612. You need the Business Insights data package for this to run without changing the source for the Allocate tools (currently Experian US - Most Recent Vintage), and need Business Insights or Location Insights to have Allocate tools.

RALEIGH PLACE

RALEIGH, NC ZIP 27612
