On a certain level, the goal of tevillat keilim is to purify utensils that we obtain from a non-Jew. However, this is not classical purification from tumah. Rather, immersing the utensil in a mikveh it is an act of a mitzva that simply models such purification.[2] This representation of the halachic mechanism of tevillat keilim helps explain some lenient halachot, such as the halacha that food placed, or even prepared, in a non-toveled utensil is unaffected by the contact.[3] However, with regard to your question, poskim seem to use this understanding of tevillat keilim to posit a stringency, which we will present after considering additional background.
If one buys a knife to use for cutting parchment, rather than for food preparation, the knife does not require tevilla.[4] The Beit Yosef[5] cites a halacha from the Hagahot Ashri that one who borrows such a knife from its owner does not have to do tevilla, even if the borrower uses it for food. This is because a borrower is obligated in tevilla only if the owner has an existing obligation. The Beit Yosef extends this logic to one who borrows a food-related utensil from a person who bought it only in order to sell it rather than to use it himself. Since the owner is not obligated to do tevilla before selling the object, neither is the one who borrows it from him. Thus, it is permitted to use the “not-purified” utensil for food if the grounds for an obligation of tevilla did not yet materialize.
The Taz[6] is not certain that the Hagahot Ashri and/or the Beit Yosef are correct. He therefore rules that one who borrows a utensil from a merchant to use for food should perform tevilla before using it, but he should do so without a beracha, since it is not certain that the tevilla is necessary. The Taz warns that due to the doubt regarding whether or not the tevilla was called for, the eventual buyer should be informed to not make a beracha when he performs tevilla after buying it. One can ask why the next owner has to do any tevilla at all, considering that the utensil already went through the “purification” process. We see from the Taz that even though a vessel was previously toveled before being sold to a consumer, the eventual buyer cannot rely on that tevilla.[7] This is because, according to the opinions that at that time there was no obligation to do tevilla, the tevilla was not effective.[8]
This must be based on the idea with which we began: Tevillat keilim is not a matter of removing impurity, which should work even if not performed in the context of fulfilling an obligation, but rather simply an act of doing a mitzva, which is effective only when done when it is in force. If and when there was no obligation of tevilla, the Taz and later Acharonim assume that not only did the borrower doing the tevilla not fulfill the mitzva, but no “purity” was achieved. Therefore, when someone later buys the item and wants to use it with food, he must perform a new tevilla.
The same applies in your case. Although you did not buy the utensils with the intention of selling them, you also did not buy them for yourself to use them for food. Therefore, according to the Beit Yosef, you do not have an obligation to tovel them before giving them as a present.[9] Therefore, the simple answer to your question is that your tevilla prior to giving the present likely does not spare or save the recipient.
Rav Tzvi Cohen[10] suggests having a third party acquire the item from you on behalf of the recipient, so that the utensil will then become obligated in tevilla (as the recipient will presumably use it for food). Then, your performing tevilla on his behalf will be effective.[11] Rav S.Z. Auerbach[12] counters that if it is not clear that the recipient will actually use it himself (e.g., he might already own such a vessel, or he might not keep it because he wishes to acquire a different kind), it is not yet defined as a utensil that is obligated in tevilla, and the tevilla would therefore not be effective. This does not mean that there is no point in doing the tevilla to help in all the cases in which the recipient clearly will use it. However, this concern may be sufficient reason for you not to recite a beracha.[13]
A similar but different solution is possible as well. You can plan to use the utensil, at least briefly, after the tevilla but before you give it to the recipient. The tevilla will thus be needed for you, and it will certainly be valid.[14]
In summary, there are various issues entailed in toveling utensils that you will give away as presents.[15] If the recipient is someone who might tovel the utensil himself, you would have to discuss the matter with him in any case, so that, assuming your tevilla works, he will not do tevilla again with a beracha, which would turn out to be a beracha l’vatala. Once doing so, you can also ask him if it would be helpful for him if you were to acquire it on his behalf and do the tevilla for him. In the average case, this would be a more recommended approach than those previously mentioned.