Why does thallium hydroxide increase the yield of product in a Suzuki reaction?
The Suzuki coupling reaction (also called Suzuki-Miyaura coupling reactions; Ref.1) is the coupling of an aryl or vinyl boronic acid with an aryl or vinyl halide or triflate using a palladium(0) catalyst similar to Heck reaction and Negishi reactions in mechanistic aspects. In particular, Negishi reaction uses organozinc reagents instead of organoboronic acids. Both reactions are powerful cross-coupling methods that allows the synthesis of conjugated olefins, styrenes, and biphenyls. The mechanism of Suzuki coupling reaction is depicted below:



The palladium catalyzed mechanism begins with oxidative addition of the organohalide ($\ce{R^1 -X}$) to the $\ce{Pd(0)}$ (e.g., $\ce{Pd(0)L_n}$) to form a $\ce{Pd(II)}$ complex (denoted in mechanism as $\ce{R^1 -Pd(II)L2X}$). It is worth nothing that this first step in both of the Suzuki and Negishi cross-coupling reactions is identical to that of the Heck reaction. This complex undergoes halide ligand exchange with the base present in the reaction mixture. 

This base is present to serve one or two possible roles: Either to react with the organoboron reagent (denoted as $\ce{R^2 -B(OH)2}$) to form a trialkoxyboronate (denoted as $\ce{^-B(OH)3R^2}$), which then attacks the palladium(II) halide complex (denoted as $\ce{R^1 -Pd(II)L2X}$), and/or to convert of the palladium(II) halide complex to a palladium(II) oxo complex (denoted as $\ce{R^1 -Pd(II)L2OH}$) that reacts with the neutral organoboron reagent ($\ce{R^2 -B(OH)2}$) (Ref.1 &amp; 2). 

Transmetalation with the organoboron reagent then follows where the $\ce{R^2}$ group of $\ce{R^2 -B(OH)2}$ replaces the hydroxide anion on the palladium(II) complex to give $\ce{R^1R^2 -Pd(II)L2}$ and boric acid. Keep in mind that organoboron compounds are highly covalent in character, and may not undergo transmetallation readily in the absence of a base. Therefore, the reaction of the base with the organoboron reagent, $\ce{R^2 -B(OH)2}$ to form $\ce{^-B(OH)3R^2}$ is very likely. Also note that transmetalation step is highly depend on the base availability and the types of ligand on the catalyst (Ref 1 &amp; 3).

Reductive elimination then follows to give the final coupled product regenerating the catalyst, hence the catalytic cycle can begin again.

Based on this mechanism, availability of a base is very important to reaction to proceed. It is clear that AP's question does not indicate the solvent used in the reaction. However, mentioned reference has been using THF as the solvent. Since solubility of $\ce{KOH}$ in THF is very low and hence its availability to the reaction. Thallium(I) hydroxide is strong base compatible with alkali bases such as $\ce{KOH}$ and key to its capability of enhancing the reaction here should be its readily availability in such solvents. This is evidence that in recent publication (Ref.4) where $\ce{KOH}$ and $\ce{TlOH}$ are equally effective in $\ce{Pd(0)}$  catalyzed coupling reaction, yield of which increases when solvent has been changed from THF to DMF.

References:


Norio Miyaura, Akira Suzuki, "Palladium-Catalyzed Cross-Coupling Reactions of Organoboron Compounds," Chem. Rev. 1995, 95(7), 2457-2483 (https://doi.org/10.1021/cr00039a007).
Karl Matos, John A. Soderquist, "Alkylboranes in the Suzuki−Miyaura Coupling:  Stereochemical and Mechanistic Studies," J. Org. Chem. 1998, 63(3), 461-470 (https://doi.org/10.1021/jo971681s).
Norio Miyaura, Kinji Yamada, Hiroshi Suginome, Akira Suzuki, "Novel and convenient method for the stereo- and regiospecific synthesis of conjugated alkadienes and alkenynes via the palladium-catalyzed cross-coupling reaction of 1-alkenylboranes with bromoalkenes and bromoalkynes," J. Am. Chem. Soc. 1985, 107(4), 972-980 (https://doi.org/10.1021/ja00290a037).
Hiroko Koyama, Hisashi Doi, Masaaki Suzuki, "Evaluation of $\ce{TlOH}$ Effect for $\ce{Pd^0}$-Mediated Cross-Coupling of Methyl Iodide and Excess Boronic Acid Ester toward Fabrication of $\ce{[^{11}C]CH3}$-Incorporated PET Tracer," Intl. J. Org. Chem. 2013, 3(3), 220-223 (DOI: 10.4236/ijoc.2013.33030).