He would be liable. A similar case appears in Mishnah Dalet, where we had a Mishnah with a machloket (dispute) between Tanna Kamma (first tanna) and Rabbi Elazar about whether a person who offers up only part of the required korban (offering) in the improper spot is held responsible. The Mishnah says, which both of them have to be burned on the Mizbeach (altar) inside, for the Minchah (meal offering) to be considered valid. If someone offered up one of them outside, which is the improper spot, the person is liable. The Tanna Kamma follows the opinion in Mishnah Dalet that a person is liable even for offering up part of the korban in the improper spot. Rabbi Elazar says that a person is not liable unless he offers up the second part as well. Both are necessary for the validity of the korban Minchah when they are offered in the proper spot. Therefore, a person would not be held responsible. He is not chayav (liable) unless he offers up both parts in the improper spot. But if he offers up one of them inside and then offers up the other one outside, Rabbi Elazar would agree that the person is chayav, that the person is liable, because offering it up outside completes the offering of what was done inside. The last part of it was done outside, so a person is liable.
If there are two spoonfuls of Levonah, of frankincense, they have to be burned on the Mizbeach in order to allow the Lechem Hapanim, the twelve showbreads that were put on the Shulchan (table) every Shabbat. They were put together with two spoonfuls of Levonah and would stay for the entire week. The two spoonfuls of Levonah would then be put onto the Mizbeach. They were offered on the Mizbeach, which made the outgoing loaves permitted to be eaten by the Kohanim (priests). So now, if only one of the two spoonfuls of Levonah that have to be burned on the Mizbeach to allow the Lechem Hapanim was offered up outside, chayav, a person would be held liable. This is the same opinion as Tanna Kamma earlier: even if part of the korban was offered up improperly in the wrong spot, it would still be chayav. Rabbi Elazar says no: the person is not liable unless he brings a second one as well. Both spoonfuls are needed in order to permit the Lechem Hapanim inside. Therefore, in order to be held responsible, you have to offer both spoonfuls outside. If he burned one of the spoonfuls inside the Beit HaMikdash and then burned the other one outside, even Rabbi Elazar would agree that the person is chayav, is liable, because he completed the Levonah service by burning the second spoonful outside.
If somebody throws part of the blood service of a korban outside, which is the improper spot, the korban usually has several applications of blood, and if he does only one of them outside, we say chayav, he is liable, even according to the opinion of Rabbi Elazar. Rabbi Elazar has continuously told us that the whole portion had to be offered in order to say that a person would be chayav here. Even if the person performs only one of the blood services—one application—Rabbi Elazar would uniquely say here that a person would be chayav even for that single application, because halacha (Jewish law) is that it is enough to validate the korban. Since it is enough to validate the korban, if it was offered up inside, it is okay. Therefore, in this scenario, where it was offered up outside, it would also be considered a person offering an acceptable korban in an improper spot, and therefore he would be chayav.
Now we’ll talk about other types of avodah (service) outside. Rabbi Elazar says that a person who pours the consecrated waters of Sukkot outside the proper spot during Sukkot is also liable on Sukkot. They would draw water every single day. The water was put into a Kli Sharet (sacred vessel) and poured on the Mizbeach. This pouring of the water is a biblical law according to Rabbi Elazar, and therefore a person who pours the consecrated water outside the proper spot is liable for performing part of the avodah outside. But this opinion belongs only to Rabbi Elazar, because Rabbi Elazar learns it out as a regular De'oraita (a biblical law) from the Pesukim (verses). But the Hachamim (sages) learn it as a Halacha LeMoshe MiSinai, that there’s no source in the actual Torah. It’s only the tradition of how it is. Therefore, in their opinion, it is not considered a violation of the prohibition against performing the avodah outside.
Rabbi Nechemiah says that if somebody offered up the remaining blood of an inner chatat (sin offering) outside by pouring it out there, the pouring out of the remaining blood of the inner chatat is considered part of the avodah. Therefore, if a person poured it out outside, he would be held responsible. The person is liable because that’s part of the avodah. It has to be poured not in the improper spot, and therefore a person would be liable.