This paper investigates the applicability of time and time-frequency features based classifiers to distinguish internal faults and other transients - magnetizing inrush, sympathetic inrush, external faults with current transformer saturation, and overexcitation - for Indirect Symmetrical Phase Angle Regulating Transformers (ISPAR). Then the faulty transformer unit (series/exciting) of the ISPAR is located, or else the transient disturbance is identified. An event detector detects variation in differential currents and registers one-cycle of 3-phase post transient samples which are used to extract the time and time-frequency features for training seven classifiers. Three different sets of features - wavelet coefficients, time-domain features, and combination of time and wavelet energy - obtained from exhaustive search using Decision Tree, random forest feature selection, and maximum Relevance Minimum Redundancy are used. The internal fault is detected with a balanced accuracy of 99.9%, the faulty unit is localized with balanced accuracy of 98.7% and the no-fault transients are classified with balanced accuracy of 99.5%. The results show potential for accurate internal fault detection and localization, and transient identification. The proposed scheme can supervise the operation of existing microprocessor-based differential relays resulting in higher stability and dependability. The ISPAR is modeled and the transients are simulated in PSCAD/EMTDC by varying several parameters.