No, the cart is not in front of the horse.
"are saved" and "doth also now save us" in the below verses have been stated in the present tense, meaning they already had been saved. However, I do agree that salvation has two parts: 1) positionally in this life being placed under the law of the Spirit of life in Christ Jesus, and 2) salvation's actual manifestation in its full form at the end of time. In order to be saved at the end of time though, one must first have been saved during their lifetime as its prerequisite.
[Rev 20:6 KJV]
6 Blessed and holy [is] he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years.
[2Co 2:15 KJV]
15 For we are unto God a sweet savour of Christ, in them that are saved, and in them that perish:
[Eph 2:5-6 KJV]
5 Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved;)
6 And hath raised [us] up together, and made [us] sit together in heavenly [places] in Christ Jesus:
[1Pe 3:21 KJV]
21 The like figure whereunto [even] baptism doth also now save us (not the putting away of the filth of the flesh, but the answer of a good conscience toward God,) by the resurrection of Jesus Christ: