It has not (so much) to do with the shape of your container, rather than the accessible volume and thus, probability of events. To quote Meldrum and O'Shaughnessy:
"Nucleation in small volumes usually gives rise to a reduction in the nucleation rate, where this can be attributed to a number factors. i) The creation of small volumes is typically associated with the exclusion of impurities that promote nucleation in bulk solution [...]. Nucleation rates can therefore approach homogeneous rates, where it is of course impossible to eliminate all interfaces. This effect can be seen in finite volumes in the µL regime and below, provided the number of droplets vastly exceeds the number of impurities present."
(loc. cit., p. 3 of 64; emphasis added).
Of course, «the other» known (and unknown) parameters affecting crystallizations interfere here as they would do for a crystallization in a bulky beaker, too (e.g., concentration, temperature/temperature gradient, etc.). A recurrent difficulty for the crystallization of organic compounds from melt indeed is the tendency to yield supercooled liquids which spontaneously may solidify/crystallize. Benzoic acid is a cheap and experimentally easy example (mp $\pu{122 ^\circ{}C}$) for this sometimes showcased in demonstration lectures. Flexible alkyl chains tend to ease the formation of supercooled liquids and subsequently, glasses instead of crystals, too.
Note that conditions optimal for the creation of crystal seeds often are not optimal for crystal growth. Energetically speaking, it is an uphill battle for flexible molecules of the melt to orderly assemble in a crystal. Even if successful, small particles formed are (if normalized for their volume) of higher energy, than larger ones, too and heat of crystallization has to be dissipated which may inhibit crystallization, too. One experiment in physical chemistry is e.g. to follow the temperature when crystallizing water to ice: at one point, temperature actually rises briefly before crystallization continues. This reflects that a crystal seed needs to grow beyond a critical radius r before there is an overall gain in free energy:
(image credit, Meldrum et al.)
The caption of this diagram reads:
"Schematic of the free energy ($\Delta{}G$) of a growing crystal nucleus as function of the radius ($r$). The energy profile is a result of the favorable volume energy ($\Delta{}G_\mathrm{V}$) and the surface energy ($\Delta{}G_\mathrm{A}$). The maximum value ($\Delta{}G_\mathrm{C}$) is achieved at the critical radius ($r_\mathrm{crit}$)." (loc. cit., p. 9 of 64)
As the authors show, the critical nucleus size $r_\mathrm{C}$ can be described by
$$r_\mathrm{C} = \frac{2\gamma{}V_\mathrm{m}} {\Delta{}\mu{}} = \frac{2 \gamma{} V_\mathrm{V}} {kT \ln S}$$
dependent on the interfacial free energy ($\gamma{}$), the molecular volume ($V_\mathrm{m}$), the chemical potential of the molecule ($\mu{}$).
Cutting/tilting the capillary just disturbed the (metastable) equilibrium reached and possibly introduced new sites where crystallization may start. (As if you scratch the inner of a beaker with a glass rod when recrystallizing a product from hot solution.) This being said, crystallization in capillaries often is a necessity if (e.g., biochem) materials of interest are scarce or/and do not form large crystals:
(image credit, access on ResearchGate)
especially if the crystals may be obtained by counter-diffusion of reagents.
Reference
Meldrum, F. C. and O'Shaughnessy, C. Crystallization in Confinement. Adv. Mater 2020, 32, 201068; doi 10.1002/adma.202001068 (an open access publication).
