I will take one word here: (f) Engineer (مهندسة) - Muhandisah. As you can see, the word ends in Ta Marbúta (ـة). This letter which is common at the end of feminine words is a combination of H and T. Meaning, in normal conditions, when you say the word alone, or when this word comes at the end of the sentence, it can be pronounced as "H". However, when the word comes in various cases, like a subject or accusative, the last letter needs to have a vowel (either A, U or I, depending on the case), and because of this, the H sound changes to T. This is one of the reasons that feminine words are written with this letter: Ta' Marbúta.
As to why it is (-tan), as I said, the spelling here is wrong, it should be (-tun). I've explained the "T" above. As for the (-un), this is called Tanwin or Nunation. It is a type of vowel in Arabic that comes usually at the end of words (nouns, adjectives) that are not defined with (AL). In other words, you cannot say (Al-Muhandisatun), this is wrong. The (-un) or (-an) or (-in) is like the A/AN in English which is added to the nouns that come without THE; indefinite. This is as simple as I can get with the grammatical issues, because Tanwin has also other uses somehow but they are deep in grammar for now.
The whole audio is wrong actually.
It should be "Lamá Muhandisatun Jadídatun".
However, away from the grammar, you can stick to the first version you typed "Lema muhendisa jadida" when speaking in some dialect form because people won't pay attention usually to the ends. But if you want a proper Arabic, it should be as I typed above.
The speech machine can't even spell the name right. It's Lamá and not Lammá.
Well, adding it to last word in the sentence is not wrong but usually we don't say it (unless a word is still expected to follow then we say it to keep the flow of speech without interruption). In the example above, the Nunation is supposed to be (-un) and not (-an) as the audio is spelling it out