On the chart for AZ Daf 38a there is a summary of Tosafos: You write that Tosafos holds according to the 2nd Lashon (Pumbedisa) that dvash & gevinah would be assur since it is Oleh Al Shulchan Melachim even thouhg it's Ne'echal chai.
I think that interpretation is inccorect. Tosafos writes clearly that the 2nd Lashon is coming to add a Kula onto the 1st Lashon, meaning the 2nd Lashon/Pumbedisa, holds of the 1st Kula as well and therefore dvash and gevinah would be muttar.
Yisrael Apfel, Queens, NY
Tosfos says that Rabbeinu Tam proved from the fact that the Gemara only lists differences between the first and second Lashon where the second Lashon is l'Kula, that we should take on both Leshonos l'Kula.
This can be explained in two different ways. We can explain that the second Lashon holds of the first Lashon, and is coming to add a further Kula, as you have understood. Alternatively, we could explain that the second Lashon argues with the first Lashon and does not hold of the Kula of the first Lashon, but the Gemara means that we should Paskan like both Leshonos l'Kula. Indeed, Tosfos ha'Rosh writes both options.
Although Tosfosdoes not clearly say which of the two explanations he means, I believe that we can infer from Tosfos that he learnt like the second explanation. Tosfos says that Rabeinu Tam ruled like both Leshonos l'Kula. If the second Lashon is adding to the first Lashon, Tosfos should have said that Rabbeinu Tam ruled like the second Lashon, which would surely have been a preferable ruling rather than relying on two opposing opinions.
Even if we say he meant as you suggest, it is still reasonable to present the chart as shown since it is intended to show the ramifications of each Kula in its own right. The footnote clarifies that l'Halachah Tosfos holds of both Leshonos l'Kula.