Term premium w.r.t. cause of inflation

The one of the primary drivers of term premium is the cause of inflation (driven by AD and AS)
“When growth and inflation is caused by strong aggregate demand, nominal bond returns are negatively correlated with growth, corresponding to low term premiums.”
“When growth and inflation is caused by strong aggregate supply, nominal bond returns are positively correlated with growth, corresponding to higher term premiums.”
I understand the relationship between of the correlations but not the corresponding high and low premiums.

My understanding is:
Increase demand (growth) → higher inflation → higher nominal interest rates → decrease in bond returns (- cor.) → investors are willing to accept lower yields for the relative safety and/or stability of longer-dated bonds (flight to quality) → thus requiring a lower term premium

Increase in supply(growth) → lower inflation → lower nominal interest rates → increase in bond returns (+ cor.) → investors need a higher term premium to be compensated to invest in longer-dated bonds

Could someone please provide some clarity on this?

Thanks