Production of exclusive dijets in diffractive deep inelastic e±p scattering has been measured with the ZEUS detector at HERA using an integrated luminosity of 372 pb-1. The measurement was performed for γ∗–p centre-of-mass energies in the range 9025GeV2. Energy flows around the jet axis are presented. The cross section is presented as a function of β and ϕ, where β=x/xIP, x is the Bjorken variable and xIP is the proton fractional longitudinal momentum loss. The angle ϕ is defined by the γ∗–dijet plane and the γ∗–e± plane in the rest frame of the diffractive final state. The ϕ cross section is measured in bins of β. The results are compared to predictions from models based on different assumptions about the nature of the diffractive exchange.