The Explanation
These questions explain that G-d did not command us to "give" an offering. That would have implied that each Jew must acquire the necessary items and hand them over to those in charge of building the Mishkan. Hashem said to separate an offering from what we already have in our possession. Thus, the only thing incumbent upon those who made the donations was to separate what they would give. In other words, we separated those items from the property we wished to donate. The treasurers of the Tabernacle would then come and take the things from us. Rashi emphasizes this point by explaining the Torah's words "an offering" as "a separation; they shall set apart from their property an offering for Me."
This is why Rashi cites Rabbi Tanchumah's explanation. The Jews owned vast amounts of gold and silver that they could donate. We received this wealth upon leaving Egypt and at the Red Sea. However, why would we have lumber? From where would it have come? Rashi explains that Yaakov prepared us for this when we left Israel to descend to Egypt. That is how it came to be that the Jews had a supply of lumber to build the Mishkan. That is why Rashi uses the unusual expression "Rabbi Tanchumah explained." Rashi was not bothered by where the Jews acquired the wood. There are other ways to explain that, as we said above. The gifts had to be separated by the donors and taken by the treasurers. Therefore, the Torah tells us that the Jews already had wood. The Jews had the objects needed for the Mishkan. Rabbi Tanchumah explains the verse itself by telling us how it came about that the Jews owned lumber.