The "Roth" ereamrod is referring to is a Roth 403b, not a Roth IRA.
The point of traditional (pre-tax) vs. Roth (after tax) accounts (whether they are 401k, 403b, or IRA) is to strategize regarding your income tax rate. If you expect to be in a higher tax bracket after retirement, a Roth style account is generally the way to go (so you pay taxes now, not later). If you expect to be in a lower tax bracket after retirement, traditional is generally the way to go (so you pay taxes later, not now). Putting money into both types of accounts is basically throwing your hands up and saying, "I'll pay taxes on some of my money now and some of it later because I have no idea." Is that really what you want? Also, I doubt that you are allowed to put $18k into *each* 403b account. It's probably $18k total between the two. If it were me, I'd pick one and not contribute to both.
Since you have no employer match in your 403b, your main benefit from that account is that it allows you to stash away more than the IRA limit of $5500. The reasons to open an IRA would be 1) you max out the $18k limit for your 403b, or 2) the fund choices or fees in your 403b account are not good. It sounds like you are currently investing in a target retirement date fund (2055), which is a fine choice as long as the fees are low. Which broker is this with? Fidelity, Vanguard, someone else...?
A taxable account should come only after you are maxing out all appropriate tax-sheltered space.
Also, for ease of conversation, few people use the "TSA" (tax-sheltered annuity) term. 403b is much more commonly understood.