Here's how I now look at things. The visuals are merely a "lens" by which one looks at the events in Trek continuity. There is absolutely nothing to prevent the entirety of TOS, for example, from happening exactly as we originally saw it, except with the visual style we are now seeing in DSC.
Similarly, from the point of view of TOS, everything that we are now seeing in DSC still happened, just in the original series style. For example, the USS Discovery (when viewed through that lens) had TOS style uniforms, jellybean controls, etc. Yet the exact same events we're now seeing, still happened.
The visuals are independent of the actual continuity. It doesn't mean parallel universes or timelines. Just different ways of interpreting the same events.