The EMTI mentioned in the query intends to issue EMTs only to CASPs within the meaning of MiCAR. 
1) In the described case, the issuance of EMTs does not create a contractual relationship within the meaning of PSD2, as there is no contract as per Article 11(3) of EMD2. The main difference between EMTs and non-tokenized electronic money (NtEM) is that EMTs do not require the holder to have a direct contractual relationship with the EMTI. At the same time, however, any holder of an EMT may, at any time, exercise their right against the EMTI to redeem the EMTs at par value in equivalent fiat currency, as set forth in Article 49(4) of the MICAR. 
The issuance and redeemability of EMTs is governed exclusively by Article 49 of MiCAR, which provides for the application of MiCAR instead of the provisions of Article 11 of EMD2. The conditions for the issuance and redemption are therefore set out in the White Paper as per Article 51 of MiCAR. Unlike NtEM, the issuance and redemption of EMTs by EMTI is not linked to the provision of a payment service, as in this case the EMTI does not maintain any payment accounts for token holders from which funds (in this case EMTs) are debited (credited).
2) Both issuance and redemption of EMTs are two bilateral legal relationships. In the case of issuance, upon payment of funds in fiat currency by the EMTI customer, the EMTI discharges its debt to the future EMT holder by issuing them an EMT at an equivalent monetary value. Similarly, in the case of redemption, the EMTI discharges its debt to the EMT holder by transferring them the equivalent monetary value of their EMT in the given fiat currency, after the EMT holder has exercised their legal right of redemption and sent the EMTs to the relevant DLT address.
3) In light of the above, Titles III and IV of PSD2 do not apply to the issuance and redemption of EMTs at all.