the philistines lived on the coast and had a string of cities there from the bronze age collapse to the eventual conquest by alexander, when they were absorbed into the new greek kingdoms in the region (the ptolemids and seleucids). they had a very big influence on the region, including influencing the religion in the generally-thought-to-be-arab enclave of petra, who worshipped a sky god named "dyushara", a clearly indo-european name that is linguistically identical to greek zeus or latin deus.
modern palestinians are descended from classical period hebrew groups, not the ancient greek philistines. you can find the odd blonde palestinian, and while they might imagine they have crusader ancestry, they're probably actually dragging around philistine dna. there was also a group that lived just outside the region, in the desert, and was called arabs by the roman and greek sources, but they weren't the same people that invaded it in the 7th century. those people that invaded are called saracens in the roman sources, are described as being "as black as the night" and migrated north from yemen. arabs were light skinned, like the jews were. the romans said the saracens were from arabia, as that is where they entered the empire from, and it took some time for the romans to understand what the fuck was actually happening, in terms of a migration event from yemen taking place. the muslims record this in their own history, as well. for the first several centuries, the roman sources actually consider islam to be a christian heresy by the desert nomads, related to the monophysitism of the egyptians. and, islam does consider jesus to have been human, like the heretical monophysite christians in the area did.
the romans did not imagine the term philistine. it was already there, and is in fact embedded in the hebrew mythology, itself. the jews were there (at least after cyrus), but the maximum extent of israel, which is something described in the oldest part of the hebrew bible, was not always reality. it's not like the romans just renamed the current state of israel to palestine. in fact, there was a historical division consisting of a north and south area, and that goes back to the assyrians, and is also noted in the hebrew bible, as well. the size of the hebrew state grew and shrunk over time as different people came in and out of the area, and the ability of the jews to project power and put vassals under their control increased and decreased; sometimes, the jews exerted authority over the other tribes, and sometimes those tribes exerted authority over them. the map wasn't set in stone by a dictate of god in the bronze age, held in place for centuries and then uprooted by the romans, like ultra-orthodox jews today would have you believe; maps are constantly changing things, in perpetual flux and evolution. history exists.
i don't know enough about classical period pottery to know who made this, but finding it somewhere in the south of the levant does not automatically make it jewish. there was a greek tribe in the area for essentially the entirety of the biblical narrative (which is a nationalist mythology and not history) and they left plenty of their own garbage there. there were also other west semitic groups, like phoenicians. an expert would be able to tell if the pottery was greek or semitic by examining it closely and the idea that it could have been "syrian or philistine" is entirely in the realm of plausibility.
the artifact should be labelled by the group they think made it and an expert should be able to determine that.