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We have used neutron spectroscopy to investigate the spin dynamics of the quantum (S = 1/2) antiferromagnetic Ising chains in RbCoCl₃. The structure and magnetic interactions in this material conspire to produce two magnetic phase transitions at low temperatures, presenting an ideal opportunity for thermal control of the chain environment. The high-resolution spectra we measure of two-domain-wall excitations therefore characterize precisely both the continuum response of isolated chains and the ``Zeeman-ladder'' bound states of chains in three different effective staggered fields in one and the same material. We apply an extended Matsubara formalism to obtain a quantitative description of the entire dataset, Monte Carlo simulations to model the magnetic order, and finite-temperature DMRG calculations to interpret the spectral features of all three phases, providing a complete understanding of the multi-faceted Ising physics of RbCoCl₃.