There is a Family Tree on Ancestry for a Thomas Tagg. This appears to be the same person as you have married to Mary Minshull.
I am always guarded about information on these trees as it can often prove to be incorrect. I will outline the details anyway and you may be able to check these for yourself.
Thomas Tagg born c1688, Chester. The year of birth is based on his age at marriage which was 20 years. He would have been a minor and parental consent would have been required.
Thomas is shown as having married twice. He died in Acton, near Nantwich in 1751 and is buried in Acton, Nantwich. The burial took place on 27 March 1751. Since there is a burial of a Thomas Tagg in St Michael's, Chester, in 1734, I would be wary of the burial in Acton.
The tree shows 7 children born to Thomas Tagg and they appear to have been baptised at St Mary, Chester. These include the baptisms of Thomas and Mary which you have given.
There are 5 other baptisms shown in the names of Tagg Check.
There are other baptisms on the Cheshire Parish Register Database in Chester St Mary, which suggest they were children of Thomas Tagg. These were as follows:
Elizabeth Tagg, D/O Thomas Tagg, 01/05/1718. Details sate that Thomas was an Attorney, Gentleman of Church Street.
Anne Tagg, d/o Thomas Tagg, on 23/07/1719. Abode: Church Street.
Elizabeth Tagg, D/O Thomas Tagg, 23/11/1720. Details state: Occupation: Gent. "At ye Churchgate".
Eleanor Tagg, D/O Thomas and Mary Tagg, 08/04/1722. Details state: Occupation Gentleman, "At Ye Churchgate".
James Tag, S/O Thomas and Mary Tagg, 29/03/1724. Details state: Occupation Gentleman. "At ye Church gate".
There is information which suggests Thomas Tagg was a Freeman of The City of Chester.
On Ancestry there are some details about taxes paid for Apprentices and there are a number of entries for Thomas Tagg. These may be worth checking out.
I don't know if the marriage of Thomas Tagg and Mary Minshull was By Banns, or By Licence. It would be an idea to see which of these it was as either way parental consent would have been required if either party was a minor. The fathers' names may be shown on the bond.
Jo.