I assume you mean 'multivariable' regression, not 'multivariate'. 'Multivariate' refers to having multiple dependent variables.
It is not considered to be acceptable statistical practice to take a continuous predictor and to chop it up into intervals. This will result in residual confounding and will make interactions misleadingly significant as some interactions can just reflect lack of fit (here, underfitting) of some of the main effects. There is a lot of unexplained variation within the outer quintiles. Plus, it is actually impossible to precisely interpret the "quintile effects."
For comparisons of interest, it is easiest to envision them as differences in predicted values. Here is an example using the R
f <- ols(y ~ x1 + rcs(x2,3)*treat) # or lrm, cph, psm, Rq, Gls, Glm, ...
# This model allows nonlinearity in x2 and interaction between x2 and treat.
# x2 is modeled as two separate restricted cubic spline functions with 3
# knots or join points in common (one function for the reference treatment
# and one function for the difference in curves between the 2 treatments)
contrast(f, list(treat='B', x2=c(.2, .4)),
list(treat='A', x2=c(.2, .4)))
# Provides a comparison of treatments at 2 values of x2
anova(f) # provides 2 d.f. interaction test and test of whether treatment
# is effective at ANY value of x2 (combined treat main effect + treat x x2
# interaction - this has 3 d.f. here)