The gemara[1] cites R. Yochanan who says that when fastening the shel yad, one makes the beracha of “… l’haniach tefillin,” and upon placing the shel rosh, he recites “…al mitzvat tefillin.” The gemara points out that R. Yochanan seems to contradict Rav Chisda’s statement that one makes a beracha on the shel rosh only if he talks in between placing the two tefillin (speaking breaks the original beracha’s efficacy regarding the shel rosh). The gemara answers that if one is silent, he makes one beracha, and if he talks, he makes two berachot. However, it is not clear what the one and the two berachot are referring to.
One approach in the Rishonim[2] is that they indicate the total number of berachot recited when putting on the two tefillin. L’hani’ach is recited before fastening the shel yad, and that should normally suffice for both. If, however, the person talks, he must recite a second beracha before donning the shel rosh. This view is accepted by the Shulchan Aruch and is the practice followed by Sephardim.[3] According to Rabbeinu Tam,[4] in contrast, the numbers one and two refer to how many berachot are said before donning the shel rosh. In other words, one always recites l’hani’ach before the shel yad and al mitzvat before the shel rosh. If he spoke, he must repeat l’hani’ach before the shel rosh, thus creating a need for a second beracha at that point (for a total of three). The Rama[5] accepts Rabbeinu Tam’s approach and establishes the minhag among Ashkenazim to follow it.
Based on your question, it is clear that you are an Ashkenazi, who recites two berachot – l’hani’ach on the tefillin shel yad and al mitzvat tefillin on the shel rosh.[6] A Sephardi recites only one beracha – l’hani’ach – before putting on tefillin, and he would say al mitzvat tefillin only if he talked in between putting on the two tefillin[7] or if he could put on only the tefillin shel rosh.[8] A Sephardi would not have made the mistake that you did, which is more likely for Ashkenazim who say al mitzvat tefillin daily. What is the halacha if an Ashkenazi recites al mitzvat tefillin instead of l’hani’ach before putting on the tefillin shel yad?
The Rosh,[9] in basic agreement with Rabbeinu Tam, says that either beracha could fundamentally apply to the shel yad or the shel rosh. However, Chazal preferred that we not recite two berachot on one mitzva, and they decided that al mitzvat was more appropriate at the end of the mitzva of tefillin. The Taz’s brother[10] says that al mitzvat pertains to the remembrances that tefillin raise and l’hani’ach applies to the mitzva’s specific detailed actions, but, again, both elements and both berachot apply to each of the tefillin.
The following halachic ramifications emerge from this generally accepted position. Since both berachot relate to both tefillin, if one recited al mitzvat at the time of putting on the shel yad and l’haniach when putting on the shel rosh, he fulfilled the berachot requirement despite the imperfect order. Therefore, says the Sha’arei Teshuva,[11] if one already recited al mitzvat and completed fastening the shel yad, he should recite the remaining beracha of l’hani’ach before putting on the shel rosh. Although some disagree,[12] this is the best solution.[13]
The matter is different if you catch your mistake before fastening the shel yad. Since l’hani’ach was, in fact, instituted to precede the shel yad and covers the shel rosh as well, you should recite l’hani’ach after al mitzvat and prior to fastening the shel yad. Then, with both berachot already recited, you should not make any beracha before putting on the shel rosh.[14] If you catch and correct the mistake quickly enough by inserting the words “l’hani’ach tefillin” within around a second and a half of saying al mitzvat, then we apply the regular rule that mistakes in berachot can be rectified toch k’dei dibbur.[15]
If a Sephardi for some reason recited al mitzvat when he made his single beracha, he has already fulfilled the requisite beracha and would not make another beracha upon putting on the shel rosh.[16]