The verb /foist/ exists. It means to pass something as if it is genuine or real or impose a fake thing as genuine. The word /foister/ doesn't exist, and it will not sound the way Trump is pronouncing it, since it will end with a schwa-(fɔɪstə), if it existed.
However, the past participle of the verb to foist is foisted. The mopheme /ed/ is a suffix used to indicate past tense in regular verbs, and it is pronounced as /id/ in standard English, but to many, it is erroneously pronounced as Trump is doing. We infer he is using the word /foisted/ because of the context. It is rather a speech sound disorder(SSD) and not a deliberate act of ignorance. The press got this wrong.
“Bonyfish beware because the same net that caught the jawless fish, caught the cartilaginous fish” (Hamilton Ayuk). Beware earthly paradise seekers because there is a serpent in every paradise"(Hamilton Ayuk). "If in this life only we have hope in Christ, we are of all men most miserable." (I Cor 15:19). "It is not how well you know a person; it is how well you treat them that they will live longer and happier with you." Hamilton Ayuk. Idle people write, idler people read, and idlest people read and whine that idle people are taking their time (Hamilton Ayuk).