This is found even in classical Latin. The perfect passive can be formed by using either the present tense of esse or, when one wants to stress the completedness of the action, the perfect tense. Likewise, the pluperfect can use either the imperfect or pluperfect of esse, and the future perfect can use either the future or future perfect.
Here's a reference for you: Gildersleeve and Lodge, Latin grammar, section 250:
The Perfect Participle passive is used in combination with sum, I am, and fui, I have been, I was, to express the Pure Perfect [that is, present perfect] and Historical Perfect [that is, preterite] of the Passive Voice. Eram, I was, and fueram, I had been, stand for the Pluperfect; and ero, I shall be, and fuero, I shall have been, for the Future Perfect.
REMARKS.—1. Fui is the favorite form when the participle is frequently used as an adjective: convivium exornatum fui, the banquet was furnished forth; fui is the necessary form when the Pf. denotes that the action is over and gone: amatus fui, I have been loved (but I am loved no longer). The same principle applies to fueram and fuero.
Simulacrum e marmore in sepulcro positum fuit; hoc quidam homo nobilis deportavit, C. Dom. 43.111; a marble effigy WAS deposited in the tomb; a certain man of rank has carried it off. Arma quae fixa in parietibus fuerant, ea sunt humi inventa, C. Div. 1.34.74; the arms which had been fastened to the walls were found on the ground. . . .
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NOTES.—1. The fui, etc., forms are rarely found in CICERO, never in CAESAR, but are characteristic of LIVY and SALLUST.
Update: Cf. Allen and Greenough, New Latin grammar, section 184, footnote 1 (p 94), which explicitly notes that this applies to subjunctive forms too:
Fui, fuisti, etc., are sometimes used instead of sum, es, etc.; so also fueram instead of eram and fuero instead of ero. Similarly in the Perfect and Pluperfect Subjunctive fuerim, fueris, etc., are sometimes used instead of sim, sis, etc., and fuissem instead of essem.