It's only in some languages including English that saying “thank you” means “I express gratitude to you”. In many languages something like “be thou blessed” is said instead. For example, in Russian “thank you” is спасибо (spasibo) [spɐˈsʲibə] which is actually a contraction of спаси Бо[г] meaning “save (you) God”.
Arabic سَلَامَات (salāmāt) is plural of سَلَامَة (salāma) “good health”. Generally speaking, there is nothing strange to say “blessings!”, or “good health to you!” or “God save you!” instead of “I appreciate you”, so why wouldn't Filipinos do that? Besides, since those phrases are actually ritual, there's no great difference in what you actually say for something good done to you, the point is to show your respect for that in a way the surrounding culture accepts.
Compare “thank you” in some other languages and note what different things it can in fact mean:
• French: merci /mɛʁ.si/ “mercy, grace”, from Middle French merci, mercy, from Old French merci, from Latin mercēdem, accusative singular of mercēs (“wages, fee, price”)
• Tibetan: ཐུགས་རྗེ་ཆེ (thugs rje che) from ཐུགས་རྗེ (thugs rje, “compassion”) + ཆེ (che, “great”)
• Mongolian: баярлалаа [pairˈɮa] “rejoice”
• Turkish (formal): sağ olun from sağ “right, alive, healthy” olun “be you”
• Moroccan Arabic: برْكة الله فيك (bərka llæh fik, literally “God bless you”), الله يبرْك فيك (llæh ibərk fik, literally “God bless you”), الله يرْحم وليدك (llæh irḥəm wəlidək, literally “God have mercy upon your parents”)
• Cebuano: salamat
• Hiligaynon: salamat