The original town, platted in 1898 and incorporated in 1920, grew slowly until the 1950s, when population jumped from about 2,500 to over 10,000 in a single decade. Large postwar residential tracts — Hampshire Gardens, Leisureville, Sterling Village — were built through the 1960s and 70s, and western expansion kept going with I-95 and Tri-Rail access in the 1980s. What that means for roofs: the housing stock nearest downtown and the coast skews older, 1950s-70s ranch and block construction, while everything from roughly the 33437, 33472 and 33473 zip ranges west is newer development, much of it built from the 1980s through the 2000s inside HOA communities. Note that a lot of that western area carries a Boynton Beach mailing address but is unincorporated Palm Beach County, not the incorporated city — worth checking before assuming which building department has jurisdiction on a given address.
Concrete and clay tile is standard on the newer western stock, with the typical wind-related tile displacement and aging underlayment issues. The older eastern neighborhoods have more asphalt shingle roofs and some flat sections over additions, where built-up or modified bitumen roofing shows up more often and ages on a different clock than the tile out west.
The main coordination issue here isn't historic review — Boynton Beach doesn't have Delray's or Lake Worth Beach's historic-district overlay — it's jurisdiction and HOA sign-off. A lot of the western tract housing sits inside planned communities with architectural review requirements on top of the permit, and addresses that read as "Boynton Beach" may actually fall under Palm Beach County's building department rather than the city's, which changes where the permit gets pulled.