Answer
When the atma (soul) leaves its gross body (sthula sharira), the subtle body (sukshma sharira) exits along with it, enveloping the soul. The subtle body contains the buddhi (intellect), manas (mind), and ahankara (ego) — all three. In that subtle body, all the cravings, hunger, thirst, etc., that existed while inhabiting the gross body continue to persist. This is what is called a "preta" (disembodied spirit). Pretas are different from bhuta and pishacha. Bhuta and pishacha are distinct species of existence — like humans, rakshasas, and yakshas — into which a being takes rebirth. Technically, bhuta and pishacha are called "deva yoni" (divine species), although they are not devatas.
The preta state is the condition that exists after the gross body has been shed and before birth into another body or species.
The atma in preta form — i.e., without having assumed any new body — sometimes remains for a very long time, sometimes even for centuries. Therefore, the arghya (offering) given to that soul by the family members does reach it, and the soul does receive it. Very few souls exist as pretas for only a brief time.
Those who are steadfast devotees of Bhagavan Hari do not remain in the preta state; rather, they are taken directly to Vaikuntha. Upon reaching Vaikuntha, they receive a "bhuvanaja" body, because their linga sharira (subtle body) has already been dissolved. Bhuvanaja sharira means a body whose nature corresponds to each particular bhuvana (realm). The shastras state that the bhuvanaja body received upon going to Shivaloka differs in nature from the bhuvanaja body of one who has gone to Vaikuntha. The bhuvanaja body received in Vaikuntha is purely sattvika, because in Vaikuntha there is no influence or entry of tamo guna and rajo guna.
Those who are Brahma-jnanis (knowers of Brahman) and whose sadhana of Brahma-jnana is complete and who have become worthy of moksha — the moment their body falls away, they become Brahma-lina (merged into Brahman). That is, along with their gross body, their subtle body also drops away instantly. They cannot become pretas. One cannot become a preta without the covering of the subtle body.
Now, regarding those ancestors who have become Brahma-lina or have gone to Vaikuntha — how will they receive your arghya? They will not be able to receive it. However, the person offering the arghya or performing the tarpana will receive punya phala (merit) because they have fulfilled their duty. And since it is impossible for you to know whether the person has reached Vaikuntha or become Brahma-lina, and as you can surmise that only the rarest of souls become Brahma-lina or go to Vaikuntha, there is more than a 90% probability that your arghya will not go to waste.
Therefore, continue performing tarpana, but do not spend excessive money on it. Some reasonable dakshina should certainly be given to the purohit (priest), because the continued existence of purohits is necessary and their livelihood must also be sustained.
And there is no absolute requirement for a purohit in tarpana either. Save your money for paropakara (benevolence) and for your own future.